







A circle, a point, and a tangent line 
20191231 

Faisal pose la question : A circle has radius 10 units and passes through the point (5,16). The xaxis is a tangent to the circle. Find the possible equations of circle? Penny Nom lui répond. 





y=lnx+(1+ln2)/2 and y=x^2 
20190128 

Mike pose la question : Prove that y=lnx+(1+ln2)/2 and y=x^2 touch each other.
The course is about logarithm and root functions... how should I solve this problem? Penny Nom lui répond. 





A tangent to a circle 
20180610 

Bellle pose la question : Determine the equation of the circle which has its center at (3,1) and tangent 3x4y+5=0 Penny Nom lui répond. 





Seven tangent circles 
20180423 

Domenick pose la question : How to calculate the circumscribed and inscribed circles formed by seven .019685 diameter circles arranged in a circle with all seven circles tangent to each other? Penny Nom lui répond. 





A tangent to a curve 
20171022 

Jasem pose la question :
Suppose that
f(x)=(3x3)^1/2.
(A) Find an equation for the tangent line to the graph of f(x) at x=2
(B) Find all values of xx where the tangent line is horizontal, and enter them as a commaseparated list (e.g., 2,3,6). If there are none, enter none.
Values of x Penny Nom lui répond. 





Two tangent circles 
20161127 

mikee pose la question : find the equation of a circle tangent to the circle x2+y2=4
and with the center at (0,5) Penny Nom lui répond. 





tan15° 
20160411 

JOHN pose la question : find the exact value of tan15° in surd form. Penny Nom lui répond. 





tan inverse 1/4 
20160314 

nazz pose la question : prove; tan inverse 1/4=1/3 cot inverse 52/47 Chris Fisher lui répond. 





A circle is inscribed in a hexagon 
20151228 

Lalitesh pose la question : A circle is inscribed in a regular hexagon ABCDEF
Prove that AB+CD+EF=BC+DE+FA Penny Nom lui répond. 





A tangent line to a parabola 
20151202 

pei pose la question : Given that the line y=mx5 is a tangent to the curve y=2x^2+3 find the positive value of M. Penny Nom lui répond. 





A common tangent to two general parabolas 
20151115 

Kind pose la question : Hi,
I want to find the common tangent of two general parabolas, but i don't know if it's possible or not.
If it's possible, please make a tutorial.
The first parabola equation : Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.
The second parabola equation : Gx^2 + Hxy + Iy^2 + Jx + Ky + L = 0.
I need this because i want to find the equation of Beloch fold. (Huzita  Hatori 6th axiom)
However if you know any other method to find Beloch folds equation, I am open for any suggestions. Chris Fisher lui répond. 





A tangent line to a circle 
20150903 

Jamie pose la question : Use the Greek method to find an equation of the tangent line to the circle
x^2+y^24x+6y+4=0 at the points (3,2square root 23. Penny Nom lui répond. 





A tangent to y = x^3 
20150531 

Brayden pose la question : Show that a tangent line drawn to the curve y=x^3 at the point (d,f (d)), where d>0, forms a right triangle with the x and y axes in quadrant 4 whose area is (2/3)d^4. Penny Nom lui répond. 





A circle is tangent to the yaxis 
20150506 

Elynna pose la question : What does it mean when a circle is tangent to the yaxis?
Thanks, Penny Nom lui répond. 





Two concentric circles 
20150421 

Juniper pose la question : Two concentric circles have radii of 4 cm and 8 cm. A segment is drawn so that it is tangent to the smaller circle and a chord of the larger circle. How long is the segment? Penny Nom lui répond. 





A tangent to y=x^3 passes through (0,2) 
20150405 

Kevin pose la question : Given that the curve y=x^3 has a tangent line that passes through point (0,2). Find the equation of the tangent line Penny Nom lui répond. 





Two parallel tangents to a circle 
20150305 

Samantha pose la question : The equation of a circle is x^2+y^2=25. Determine
the equation of the parallel tangent lines to this
circle, for which the slope is 4/3. Penny Nom lui répond. 





A tangent to a circle 
20141222 

azman pose la question : Find the equation of the tangent line to the circle x^2+y^2=9 at the point P (2, square root of 5). Penny Nom lui répond. 





A tangent to a curve passing through a point not on the graph 
20140915 

Aquilah pose la question : For the curve y = x2 + 3x, find the equations of all tangent lines for this graph
that also go through the point (3, 14). Penny Nom lui répond. 





A tangent of the curve (x/a)^n+(y/b)^n =2 
20140415 

sudhir pose la question : the equation of tangent of the curve (x/a)^n+(y/b)^n =2. at(a,b) is Penny Nom lui répond. 





Two circles that touch each other externally 
20140408 

Ameya pose la question : Two circles of radii a and b (a > b) touch each other externally. ST is a common tangent touching the circles at S and T respectively, then ST^2 is equal to Chris Fisher lui répond. 





A circle which is tangent to two perpendicular lines 
20140309 

MJ pose la question : I'm a College Student taking up Bachelor of Secondary Education on Math Subject.
And I'm struggling for my research about Circles. I done solving the said topic particularly on this question:
"What are the possible equations of a circle being tangent to a pair of perpendicular lines, having the origin as the Point of Intersection and the C (h, k), where h, k ∈ℤ"
But I can't get what would be the process that I must do in order to jive to my idea/goal for that problem.
Please check my idea that the numerical coefficients of the equation is equal to the radius of the circle.
Thanks in advance! :) Penny Nom lui répond. 





Four tangent circles 
20131009 

Nilesh pose la question : Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. How to find the area of the space enclosed by the four pieces?
Please let me know. Robert Dawson lui répond. 





Equal ordinate and abscissa 
20130815 

sonit pose la question : the slope of tangent to the curve y=(4x^2)^1/2 at the point, where the ordinate and abscissa are equal, is Penny Nom lui répond. 





A triangle and an incircle 
20130509 

Max pose la question : On my Geometry Test about tangent, chord, and secant lengths, my teacher gave an extremely difficult problem.
It was a Circle inscribed in a Triangle with all triangle sides being tangents and lengths were given. My class was told to find the length of each segment of the line.
The points on each line were the vertexes of the triangle, and the point where the line hits the circle.
Please explain how someone could do this. Chris Fisher lui répond. 





Tangents to the curve y = x^3 
20130324 

Ethan pose la question : How many tangent lines to the curve y = x^33 pass through the
point (2, 4)? For each such line, and the exact coordinates of the point of
tangency on the curve. Penny Nom lui répond. 





Trigonometry 
20130323 

Tizoc pose la question : I am in a trig class and I have a conflict. When solving the length of a side, I know what trig function to use, but I do not know what angle to use in a calculator. To make this a little more understandable, if I have all the angles available in a right triangle and I use the tangent function, how do I know what to use?
Heres what I do not know what to put in my calculator: Tan(?)
Thanks in Advance! Penny Nom lui répond. 





The tangent to a circle at a point on the circle 
20130222 

Andrew pose la question : What is the equation of the line tangent to the circle with equation x^2+y^2=25 at the point (4,3) Penny Nom lui répond. 





Four tangent circles 
20121004 

renu pose la question : inside of a circle K of radius length measure R,three circular discs A,Band C each of radius r are placed so that each touches the other two and K . express R in terms of r. in the space between K, A and B , another circular disc D is placed which just touches K, A and B. if the radius is s, show that (6+root3)s=(2+root3)r Penny Nom lui répond. 





A tangent to f(x) = 1/x 
20120904 

Steven pose la question : Consider the graph of the function f(x) = 1/x in the first quadrant, and a line tangent to f at a point P where x = k. Find the slop of the line tangent to f at x = k in terms of k and write an equation for the tangent line l in terms of k. Penny Nom lui répond. 





A tangent line to a circle 
20120414 

Novelyn pose la question : find an equation of the line tangent to a circle with equation x^2+y^2+6x8y27=0 at the point P(1,2) Penny Nom lui répond. 





Tangent of theta 
20120117 

stahl pose la question : explain what the 'tangent of theta' means. Draw and label a diagram to help with your explanation. Harley Weston lui répond. 





An equilateral triangle and some circles 
20120110 

tushar pose la question : draw an equilateral triangle with side 6cm.draw 3circles with radii 3cm on each angular point of triangle.draw common tangent on each of two circles Penny Nom lui répond. 





Lines tangent to y^2=4x 
20111111 

Reuchen pose la question : Find equations of the lines tangent to y^2=4x and containing (2,1). Penny Nom lui répond. 





One central circle and three tangent circles 
20111016 

Margaret pose la question : You have one central circle and three or more circles tangent to the outside of the circle of varying radii. You know the x,y coordinates of the centers of the other circles. If you now remove that central circle (and pretend you never knew where it was), can you calculate its center in x,y coordinates? Chris Fisher lui répond. 





A tangent to the earth 
20110903 

Vickram pose la question : I have a math problem regarding tangent and circle. My example is as
follows: if a long flat ruler measuring 1500 miles is placed on top of earth
which has a radius of 3960 miles what part (length) of the tangential ruler
will actually be touching the earth and what two parts will not? Chris Fisher lui répond. 





Three tangent circles 
20110821 

maribie pose la question : three discs are tangent externally distances between their centers are 23cm, 15cm, and 20cm. find their radii.t Penny Nom lui répond. 





Three tangent circles 
20110819 

hanniel pose la question : two coin are tangent to a third coin internally and are tangent to each other
externally. The distance between their centers are 14 mm, 17mm, and 5mm.
find their radii Penny Nom lui répond. 





A line tangent to f(x)=1/x 
20110605 

Michael pose la question : A line tangent to f(x)=1/x in the first quadrant creates a right triangle
with legs the xaxis and the yaxis. Prove that this triangle is always
2 square units regardless of where the point of tangency is. Penny Nom lui répond. 





Three tangent circles 
20110501 

mark pose la question : Three circles of radii 24 cm, 32 cm, and 42 cm are externally tangent to each
other (each is tangent to the other two). Draw a diagram and using the Law of
Cosines find the largest angle of the triangle formed by joining their centres. Penny Nom lui répond. 





A family of circles 
20110301 

steffi pose la question : Find the equation of the family of the circle passing through the the point of intersection of x^2+ y^2 4x28=0 and x^2 +y^2 4x20+52=0; the member tangent to x=7. Penny Nom lui répond. 





Two tangent circles 
20110209 

xhesika(jessica) pose la question : Two circles of radius 10 are tangent to each other.A tangent is drawn
from the centre of one of the circles to the second circle.To the nearest
integer find the area of the shaded region. Penny Nom lui répond. 





A tangent to a circle 
20110206 

debz pose la question : what is the formulae of the tangent to a circle.... our teacher gave us a lot of homework.. and she ask us to find the formulae by ourselves.. Penny Nom lui répond. 





Tan(x+pi)tan(pix)=2tan(x). 
20110109 

Steven pose la question : Verify the identity:
Tan(x+pi)tan(pix)=2tan(x) Penny Nom lui répond. 





A tangent line 
20110103 

Amanda pose la question :
Question from Amanda, a student:
an equation of the line tangent to y=x^3+3x^2+2 at its point of inflection is
(A) y=6x6
(B) y= 3x+1
(C) y= 2x+10
(D) y=3x1
(E) y=4x+1 Penny Nom lui répond. 





The equation of a circle 
20100504 

crystal pose la question : find the standard form of the circle with center (2,3) and tangent to the line y=1 Penny Nom lui répond. 





A tangent line to a circle 
20100415 

Rhonda pose la question : The Greek method for finding the equation of the tangent line to a circle used the fact that at any point on a circle the line containing the reauis and the tangent line are perpendicular. Use this method to find an equation of the tangent line to the circle x^2+y^2=9 at the point (1,2 square root of 2). Penny Nom lui répond. 





The equation of a circle 
20100218 

AHMED pose la question : find the equation to the circle with centre at the point (1,1) and touching the straight line 5x+12y=7. Penny Nom lui répond. 





Angle of incline 
20100120 

Alan pose la question : how do I fnd the angle of an incline with a measurement of 0.042 with an adjacent of 1.2mtrs?. Thank You Penny Nom lui répond. 





A circle problem 
20091214 

Fawad pose la question : AP is a tangent at P to a circle centre O, where AP=6cm. The straight line AQC is such that QC= 9cm.
Find the length, in cm of AQ. Chris Fisher lui répond. 





f(x)=x+2sinx 
20091212 

amroziz pose la question : for which values of x does the graph of f(x)=x+2sinx have horizontal tangent Harley Weston lui répond. 





The triangle formed by the tangent and the coordinates axes 
20091123 

Nirmala pose la question : Given that y=1/x, x is not equal to zero. Prove that the area of the triangle formed by the tangent and the coordinates axes is 2. Harley Weston lui répond. 





Three circles 
20091002 

Brandon pose la question : There is a quarter circle with a radius of 1. along one eged of it,
there is a semicircl with a diameter of 1, and its center is on the
drawn line. there is another semicircle again with the center on the
other drawn line, and this one has an unknown diameter of X. both
circles are internally tangent, and are tangent to each other. Find X. Robert Dawson and Chris Fisher lui répond. 





A line tangent to a parabola 
20091001 

kanchan pose la question : for what value of c a line y=mx+c touches a parabola y^2=4a(xa) Penny Nom lui répond. 





A tangent to a circle 
20090714 

Eric pose la question : Hi I am trying to complete a packet that has a list of questions to brush up on precalculus skills. The question asks "For the circle x^2 +y^2 + 6x  4y + 3 = 0 find : the equation of the tangent at (2,5). I have already found the equation for the circle and standard form and the center and radius. However, i do not know how to find the slope or yintercept of the tangent line. Please help. Thanks. Stephen La Rocque lui répond. 





4 tan(360/(2n)) 
20090518 

molly pose la question : in the formula to find the area of any regular polygon how do you figure out 4tan part of the formula Penny Nom lui répond. 





A common tangent to two curves 
20090302 

Jay pose la question : For what values of a and b will the parabola y = x^2 + ax + b be tangent to the curve y = x^3 at (1,1)? Penny Nom lui répond. 





A point on 8x^2+5xy+y^3=149 
20090204 

Vivian pose la question : Consider the curve defined by 8x2+5xy+y3=149
a) find dy/dx
b) Write an equation for the line tangent to the curve at the point (4,1)
c) There is a number k so that the point (4.2,k) is on the curve. Using the tangent line found in part b), approximate the value of k.
d) write an equation that can be solved to find the actual value of k so that the point (4.2,k) is on the curve
e) Solve the equation found in part d) for the value of k Harley Weston lui répond. 





Two tangent circles 
20090123 

Murtaza pose la question : Two circles touch externally at T. A chord of the first circle XY is produced and touches the other at Z. The chord ZT of the second circle, when produced, cuts the first circle at W. Prove that angle XTW = angle YTZ. Robert Dawson and Chris Fisher lui répond. 





A cyclic quadrilateral 
20090123 

Murtaza pose la question : Line ATB touches a circle at T and TC is a diameter. AC and BC cut the circle at D and E respectively.Prove that the quadrilateral ADEB is cyclic. Robert Dawson and Chris Fisher lui répond. 





1 foot drop every 25 feet 
20090122 

jerry pose la question : 1 foot drop every 25 feet what is the angle of the degree Penny Nom lui répond. 





Two tangent circles and common tangents 
20081201 

Alan pose la question : Radius of big circle 30cm, radius of small circle 10 cm. From the diagram, the radius from the tangent do not form a semicircle but at an angle. Find the perimeter of the band around both the circle. May need to use trigonometry to find reflex angle AOB, CMD and get the major arc length AB and minor arc length CD Penny lui répond. 





Two tangents to a circle 
20081126 

rogerson pose la question : The length of the tangent to a circle is 15 cm. If the angle between the two tangent lines to the circle is 28 degrees, what is the radius of the circle? Penny Nom lui répond. 





Tan(3x) 
20081123 

Evan pose la question : Derive an expression for tan3x in terms of tanx Harley Weston lui répond. 





A circle tangent to a line and with its centre on another line 
20081101 

liza pose la question : Find the equation of the circle of radius squareroot 26 tangent to the line 5x+y=13 and having its center on the line 3x+y+7=0. Chris Fisher lui répond. 





Tangent line 
20081027 

Maddie pose la question : Find a general equation for a line that touches, but does not pass through the function Y=X2(X squared) + BX+C. Stephen La Rocque and Victoria West lui répond. 





Two tangent lines to a parabola 
20081026 

Marcus pose la question : Show that the tangent lines to the parabola y = ax^2 + bx + c at any two points with xcoordinates p and q must intersect at a point whose xcoordinate is halfway between p and q. Penny Nom lui répond. 





The slope of a tangent line 
20081018 

Amanda pose la question : If f(x)=square root of (x+4), and the slope of the tangent line at x=21 was 1/n for some integer n, then what would you expect n to be? Stephen La Rocque lui répond. 





A tangent line to f(x) = 1/(x  1) 
20081016 

Amanda pose la question : If f(x)=1/(x1) then what is the slope of the tangent line at x=2? Harley Weston lui répond. 





How many parallel tangents may a circle have? 
20080929 

Manish pose la question : how many parallel tangents may a circle have? the text book shows two.but a circle can have infinite tangents.then why not parallel tangents coz
theoretically each tangent have a parallel tangnts then no. of parallel tangent a circle may have is equals to half of the infinity i.e. infinity.. Walter Whiteley lui répond. 





Parallel Tangents 
20080924 

manish pose la question : how many parallel tangents may a circle have? the text book shows two.but a crcle can have infinite tangents. Janice Cotcher lui répond. 





A tangent to a circle 
20080906 

Jake pose la question : Find an equation of the line that is tangent to the circle x^2 + y^2 = 3 at the point (1,√2) Penny Nom lui répond. 





Two tangent circles 
20080822 

Michele pose la question : A circle of radius 2 is externally tangent to a circle of radius 8,
How do you find the length of their common tangent. Penny Nom lui répond. 





Irregular polygon and Circle that Intersects All Sides 
20080820 

Xetro pose la question : Hi,
Suppose you have an irregular polygon(convex or concave) with n > 3 sides.
The question is  Find some circle that will cut(in limiting case  touch) all the sides of that polygon.
It doesnt matter how many times it cuts the side(1 or 2), it just have to cut or touch it.
How to find such a circle? or how to decide if such circle even exists?
What if those segments do not form a polygon but are some arbitrary segments ?
Really want to know how to do it................
Thanks a lot..
Regards,
Xetro Janice Cotcher lui répond. 





Area of triangle formed by three tangent circles 
20080731 

brian pose la question : Three circles with radii 3,4 and 5 touch each other. The circles are tangent to each other. What is the area of the triangle formed by the centers of the circles? Stephen La Rocque lui répond. 





A tangent to a curve through a point not on the curve 
20080723 

Carter pose la question : How does one find the tangent points on a curve, given only the curve's function
and the xintercept of that tangent line?
i.e. Find the point(s) on the curve y = (x^2) + 1, where the tangent line passes
through the point (2, 0).
I know that there will be two such points, one where y is very close to 1, and the
other point where y is a large negative number. However, I do not recall how to
figure out the tangent line equation given a single intercept and solving to find the
tangent points. Penny Nom lui répond. 





A tangent line to a circle 
20080709 

Rita pose la question : The tangent to a circle may be defined as the line that intersects the circle in a single point, called the point of tangency. If the equation of the circle is x^2 + y^2 = r^2 and the equation of the tangent line is y = mx + b, show
r^2(1 + m^2) = b^2 Harley Weston lui répond. 





A space camera circles the Earth 
20080616 

Rita pose la question : A space camera circles the Earth at a height of h miles above the surface. Suppose that d distance, IN MILES, on the surface of the Earth can be seen from the camera.
(a) Find an equation that relates the central angle theta to the height h.
(b) Find an equation that relates the observable distance d and theta.
(c) Find an equation that relates d and h.
(d) If d is to be 3500 miles, how high must the camera orbit above Earth?
(e) If the camera orbits at a height of 400 miles, what distance d on the surface can be seen? Penny Nom lui répond. 





tan(4a  b) 
20080612 

A student pose la question : hi guys just a quick help on question needed thanx
if tan a = 1/5 and
tan b = 1/239
find value of tan(4ab)
thanks alot in advance Harley Weston lui répond. 





Three mutually tangent circles 
20080604 

Jacob pose la question : If three circles are mutually tangent, does that mean that the two tangent lines are perpendicular? Chris Fisher lui répond. 





How many bricks I can place around a 26inch circle? 
20080522 

Jon pose la question : I want to know how many bricks I can place around a 26inch circle? There must be a formula other than trial and error. The length of the bricks is 6inches. [How many 6inch tangents can be in a 26inch circle?
Thank you very much.
Jon Harley Weston lui répond. 





A tangent to two circles 
20080413 

erson pose la question : find the length of the tangent segment AB to two circles whose radii are a and b respectively, when the circles touch each other.
the illustration looks like this...hope you'll understand...
there are 2 circles  one is big one is small. they touch each other. and there is this irregular 4 sided polygon that connects them...there is a line that connects them from their center point and another from the tip of the circles...and that's it...i cannot explain very well
please bear with me Stephen La Rocque lui répond. 





A tangent to a circle 
20080413 

rogerson pose la question : Line t from point P is tangent to circle O at T, the point of tangency. Find the length of PT when the radius of the circle is 5cm and the distance between points P and O is 8cm. Stephen La Rocque lui répond. 





The equation of a circle 
20080205 

aime pose la question : Find the equation of the circle tangent to 3x+4y15=0 at P1(1,3) and passing through P2(6,3) and P3(0,5)? Stephen La Rocque lui répond. 





A tangent to a circle 
20080104 

adam pose la question : Find a>0 so that the line y=x+a is a tangent to the circle x^2 +y^2=2. Stephen La Rocque and Harley Weston lui répond. 





Lining up coins visually using geometry and trigonometry 
20071231 

Jessica pose la question : a) In what order would you arrange a penny, a nickel, a dime, a quarter, and a halfdollar so that they all have the same apparent size? The diameters of the coins, in thousandths of inches, are as follows: penny, 750; nickel, 835; dime, 705; quarter, 955; halfdollar, 1205.
b) How should the coins be placed, if the distance between the dime and the halfdollar is 100 units?
How far from thw dime should your eye be to see that all the coins have the same apparent size?
c) What angle do the coins subtend when they have the same apparent size? Stephen La Rocque lui répond. 





The tangent to a curve 
20071210 

Christy pose la question : I know this question is simple but I can't figure out what I'm doing wrong.
Find the equation of the tangent line to the curve 2x^2  y^4= 1 at the point (1,1). Penny Nom lui répond. 





A triangle and a pentagon 
20071208 

Olivia pose la question : A regular pentagon has an area of 800 square centimetres. What is the area of the triangle extended from one side of the pentagon? Stephen La Rocque lui répond. 





A particle moves in the xyplane 
20071112 

Russell pose la question : A particle moves in the xyplane with
X = 2t^3  12t^2 + 18t
Y = 3t^4  28t^3 + 72t^2
find an equation of the line tangent to the given curve at t_0_ = 1
note: t_0_ is t subscript 0 Harley Weston lui répond. 





Equation of a tangent line to a function 
20071004 

Princess pose la question : If f ' (x) = 3x^2 +1, find the equation of
the tangent line to f(x) = x^3 + x at x= 1. Stephen La Rocque lui répond. 





A tangent line to a circle 
20070926 

Randy pose la question : Find the equation of the tangent line at coordinates (1 , 4)
on the circle x^2 + y^2  4x  21 = 0
I would like to learn the fastest way to relate any coordinates of a circle
to any possible point of tangency. Stephen La Rocque lui répond. 





The tangent to y = x^3 at x = 0 
20070904 

Amit pose la question : consider the equation = x^3. The equation of tangent to this curve (which is smmetrical in Ist and IVth quadrant) at (0,0) is y=0, which is xaxis.
but graphically one can visulize that xaxis intersects the curve, so how can it be the tangent to the curve. Please help. Harley Weston lui répond. 





A circle and a tangent 
20070827 

Lindsay pose la question : Hello. I'm trying to do a math problem and have searched the internet for equations but have come up empty handed. If you could help, that would be greatly appreciated!
The problem is stated thus: A circle is tangent to the yaxis at y=3 and has one xintercept at x=1.
a. Determine the other xintercept
b. deduce the equation of the circle. Penny Nom lui répond. 





Twocolumn proof for a circle geometry problem 
20070824 

Kendra pose la question : i have to prove that tangents to a circle at the endpoints of a diatmeter are parallel by stating whats given, whats to prove and a plane, then write a two column proof i dont understand this Stephen La Rocque lui répond. 





Tangents to a circle 
20070818 

Laura pose la question : I have tangents from point A and B that intersect at C. A third tangent XY lies in between the two lines that I have already drawn. I measured the perimeter and then I drew another line that was tangent to the circle and was inside the two lines again and measured the perimeter again. The perimeters were the same but I don't know how to prove why this happened and write a theorem for it. Chris Fisher lui répond. 





Two circles C1 and C2 meet at the points A and B 
20070815 

Jerry pose la question : Two circles C1 and C2 meet at the points A and B. The tangent to C1 at A meets C2 at P. Point Q inside C1 lies on the circumference of C2. When produced, BQ meets C1 at S and PA produced at T. Prove that AS is parallel to PQ. Chris Fisher lui répond. 





Circle Geometry 
20070814 

Robin pose la question : In a triangle ABC, angle A=75 and B=60. A circle circumscribes the triangle. The tangents of the at points A and B meet in a point D outside the circle. Show that ABD is an isosceles triangle with a right angle at D. Diagram included. Stephen La Rocque lui répond. 





Diagonals on a cylinder 
20070810 

John pose la question : I have a cylinder that is 37.5" width X 25.25" circumference. I need to create a repeating diagonal lined pattern on the cylinder so that when it prints it joins perfectly at the circumference repeat. The design must follow these specs.
Black diagonal lines need to be 1.250" max width X 1.5" max spacing between the black lines.
Please Help Stephen La Rocque lui répond. 





Two tangent lines to y=x^3 
20070607 

stephanie pose la question : find the equations of two tangent lines to the y=x^3 function through the point (2,8) Penny Nom lui répond. 





Finding the hypotenuse without Pythagorus 
20070511 

Shelbie pose la question : How do i find the hypotenuse of a right traingle not using the pythagorean thereom if i have the measurements of the legs? Stephen La Rocque lui répond. 





Two tangents to a circle 
20070417 

Doug pose la question : Two distinct, nonparallel lines are tangen to a circle. The measurement of the angle between the two lines is 54 degrees (angle QVP).
Suppose the diameter of the circle is 2 cm. What is the distance VP? Suppose the distance VP is 3.93 cm. What is the diameter of the circle? Find a formula for d, the diameter of the circle, in terms of VP.
Find a formula for VP in terms of d, the diameter of the circle. Stephen La Rocque lui répond. 





The angles in a right triangle 
20070328 

Golaan pose la question : I need the to understand the formula for finding either of the acute angles of a right triangle given it's hieght length and base length.
I want to find the degrees of either accute angle. So for this example I have a right triangle with a height of 410 meters and a base length of 1,700 meters.
I don't understand cosine, sine, and tangent or the other ones at all. So if the solution includes those (which I believe it does) could b very verbose yet in a very elementary way?
The purpose of ths is that I have to define the general incline angles (or grade) of various areas of terrain. I know the distance by map and also the the altitude at either endpoint. Penny Nom lui répond. 





Triple angle tangent formula 
20070315 

sam pose la question : Hi I am trying to derive a triple angle formulae for tan. I know i need to use compound and double angle formulae but am finding it difficult to "clean" up my fraction to get the triple angle formulae can you show me a worked derivation?! thanks Penny Nom lui répond. 





Angle of elevation 
20070313 

Joslyn pose la question : A ship at sea sights a 12m high lighthouse on a cliff which is 80m above sea level.
If the angle of elevation to the top of the lighthouse is 27 degrees, calculate the distance from the ship to the shore. Haley Ess lui répond. 





Finding the equation of the circle 
20070220 

ning pose la question : Given the radius of a circle square root of 10 tangent to the line 3x+y+19 = 0 and passing through (0,3), how can i solve the equation of circle? thank you... Chris Fisher, Steve La Rocque and Penny Nom lui répond. 





A common tangent line 
20070220 

chris pose la question : I have this problem I have been working on for days and cannot figure it out. it states: Find the two points on the curve y=x^4  2x^2  x that have a common tangent line.
I know you use the first derivative to find the tangent line so if it is a common tangent line should you find two of the exact same tangent line equations at two coordinate points? Chris Fisher lui répond. 





Circle geometry 
20061119 

Namrata pose la question : AB is a diameter and AC IS A CHORD OF A CIRCLE SUCH THAT angle=30. the tangent at C intersect AB produced in a pointD. Prove that BC=BD. Stephen La Rocque lui répond. 





Tangent lines 
20061109 

Melissa pose la question : let f be a function with f(1)=4 such that for all points (x,y) on the graph of f the slope is given by (3x^(2)+1)/(2y)
a.)Find the slope of the graph of f at the point where x=1. b.)Write an equation for the line tangent to the graph of f at x=1 and use it to approximate f(1.2) c.) Find whether f is concave up or concave down when x=1. Is your answer in part b an overestimate or an underestimate? Stephen La Rocque lui répond. 





How high (in feet) is the mountain? 
20060829 

Briana pose la question : A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 29 degrees. From a point 2000 feet closer to the mountain along the plain, they find that the angle of elevation is 31 degrees.
How high (in feet) is the mountain? Stephen La Rocque lui répond. 





A tangent to a circle 
20060705 

Izumi pose la question :
I have problems finding the point of tangency between the circle C
x^{2} + y^{2} + 4x  6y  12 = 0
and the tangential line that passes through the point P (6, 1).
Stephen La Rocque lui répond. 





The interior angles of a right triangle 
20060520 

Greg pose la question : I am wondering if there is a way to figure out the interior angles of a right triangle if we know ONLY the side lengths, and the trick is, we CANNOT use arctangent! Leeanne Boehm and Penny Nom lui répond. 





Geometry proof 
20060423 

Jade pose la question : From a point P outside a circle with centre O, tangents are drawn to meet the circle at A and B.
a) Prove that PO is the right bisector of the chord AB.
b) Prove that Stephen La Rocque lui répond. 





Two circles 
20060407 

Louisa pose la question : One circle of radius 7cm is touching another circle of radius 4cm. These circles are on a line and the problem is to find the length AB where A is the point marking the bottom of the radius of one circle and B is the point marking the bottom of the radius of the other circle. Stephen La Rocque lui répond. 





A sequence of circles and tangents 
20060116 

Paul pose la question : Consider a circle whose center is (2,2) and whose radius is 1, and the
straight line that goes through the origin and that is tangent to this
circle so that the intersection between them is as shown in the attached
picture. With this new point we make a new circle whose radius is half
of the first one, and we calculate the corresponding intersection point
with the same suppositions as in the first case. We repeat the process
to the infinite. Find the distance between the center of the circle in
the infinite and the origin (point (0,0)). Chris Fisher lui répond. 





Four tangent circles 
20051206 

Ananth pose la question :
I have one bigger circle A with radius 15.
Inside this bigger circle i have another circle B with radius 3 which touch this bigger circle. Have another circle C with radius 4 which touches A and B. I would like to draw a biggest circle which touches A,B and C.
Chris Fisher lui répond. 





A tangent to a parabola 
20051102 

A student pose la question : Find the point on the curve y=x^{2} where the tangent to the curve is parallel to the secant line connecting (1,1) and (2,4) Penny Nom lui répond. 





Two tangents to a circle 
20050618 

Tej pose la question : The tangents drawn from points M and N of a circle
having centre O intersect each other at point P. If
angle MPN=60 degrees, NM=10, then find the radius of
the circle and Area of quadrilateral OMPN. Penny Nom lui répond. 





Tangents to a circle 
20050319 

Sue pose la question :
You're given the equation to a circle (x3)^{2 }+ (y3)^{2} = 4
and you need to do 3 things:
1. Find a point on the circle
2. Construct an equation for a tangent line to the circle and through the point
3. Plot the circle, point and the tangent line on one graph
Penny Nom lui répond. 





Three tangent circles 
20050125 

Kate pose la question : Two circles, C1 and C2, touch each other externally; and the line l is a common tangent. The line m is parallel to l and touches the two circls C1 and C3. The three circles are mutually tangent. If the radius of C2 is 9 and if the radius of C3 is 4, what is the radius of C1? Chris Fisher lui répond. 





The tangent line at an inflection point 
20041128 

Louise pose la question : the equation of the tangent line to the curve y = x^{3}  6x^{2} at its point of inflection is... Penny Nom lui répond. 





A common tangent line 
20041005 

Shanup pose la question : The xaxis is a common tangent of y = x^2 and y = x^3. Find the equation of another common tangent. Penny Nom lui répond. 





A tangent to a hyperbola 
20040802 

A student pose la question : The equation of a hyperbola is 32x*2 18Y*264x +72y +248=0. The equation of a tangent line to this hyperbola is y= (16/15)X + 10/3 I have been trying to find the point where this line intersects the graph. What I did was solve for x and then plugged in the result into the equation of the hyperbola, but I am getting two answers and I am supposed to get only one because the line is tangent to the graph. For this reason, I would like to know what I am doing wrong or what I have to do to know which answer is correct. Penny Nom lui répond. 





The tangent of theta 
20040710 

Jacob pose la question : P is a point on a unit circle with coordinates(0.6,0.8). Find tan of theta. My book shows me how to do it,"tan of theta=opp./adj.=0.8/0.6=4/3,"and leaves it as that's the answer(4/3).When do we know from a problem to find the angle measure (in this case, the angle measure of theta) and how do we know when to give something like 4/3 without converting it to the angle measure? Penny Nom lui répond. 





A tangent to a quadratic 
20040604 

Jem pose la question : I have a question on the tangent to a quadratic curve.
Say I have a curve y = ax^{2} + bx + c. The gradient, using the derivative of y, at any point x on the curve is: 2ax + b right? Then, for the tangent that cuts the curve at a point x, the equation of the tangent can be: y1 = (2ax + b)x1 + d.
My question is, how is the point d of this tangent determined? It is the point on the yaxis where the tangent cuts isn't it? Is there a formula for it? Penny Nom lui répond. 





The center of a circle 
20040526 

Wan pose la question : I am trying to find the radius of an arc. The only things i know about the arc is all referenced from the line of tangency to the arc. on both sides i have a differnt horizontal perpendicular distance to the point of tangency.
left side * right side (*=point of tangency). Then i have 2 difference vertical perpendicular distance of the end points to the line of tangency. I know it sounds very bad in text but this is all i know about the arc. Can you help me find the radius? Penny Nom lui répond. 





A geometry problem 
20040304 

Jennifer pose la question : I need help with this problem: Square ABCD has side length 2. A semicircle with diameter AB is constructed inside the square, and the tangent to the semicircle from C intersects side AD at E. What is the exact length of CE?o Chris Fisher lui répond. 





The sketch of a graph 
20031007 

A student pose la question : I was wondering how do you figure out if a graph has a horizontal tangent line. One of my homework problem was to sketch the graph of the following function; (4/3)x^{3}2x^{2}+x. I set f''(x) ( the second derivative) of the function equal to zero and got the inflection point:(1/2,1/6). Also i am having trouble finding the concavity for x>1/2 and x<1/2, i am getting a different answer from the back of the book, the graph i draw looks completely different from the correct answer. Penny Nom lui répond. 





The slope of a tangent 
20031001 

A student pose la question :
find the slope of the tangent to each curve at the given point f(x)=square root 16x, where y=5 Penny Nom lui répond. 





A theorem in geometry 
20030902 

Diego pose la question : Please refer to figure in attached file. P is a point on the chord AB of a circle such that the tangent PT which touches the circle at T is equal to AB. How do we prove that PT^{2} = AP x BP. Dieter Ruoff and Penny Nom lui répond. 





sin theta = 7/8 
20030507 

Patty pose la question : If sin0 = 7/8 and 0 is in quadrant 2, find the other five trigonometric functions of 0. (report your answers in radical form) Penny Nom lui répond. 





A circle, tangent to two circles and a line 
20030430 

Keith pose la question : I have a horizontal line (that is treated as a datum line or the X axis), with two circles having their center points at different heights from that line (X1,Y1 & X2,Y2). The two circles are also at different diameters (R1 & R2). Both circles and the line (XAxis) do not intersect nor are they tangent. My goal is to determine the maximum diameter of an inscribed circle that will fit between all three. Chris Fisher and Harley Weston lui répond. 





A tangent to a circle 
20030418 

Lech pose la question : The line with equation y=mx is a tangent to the circle with equation x2+y26x6y+17=0. Find the possible values of m. Harley Weston lui répond. 





Trigonometry problems 
20021201 

Chiara pose la question :
 Find tan 35pi/4
 Graph y = cos^{2}x  2sinx
Penny Nom lui répond. 





Constructing a tangent to two circles 
20021128 

Tom pose la question : I have two circles, different sizes a known distance from each other. We know the radii of the circles. How do I construct a line that is tangent to both circles relative to the segment that connects the centers of both circles? Chris Fisher and Penny Nom lui répond. 





The tangent to a curve and the tangent of an angle 
20020826 

A teacher pose la question : Is there a relationship between the tangent of a curve(line touching the curve at one point) and tangent (the trigonometric function)? Chris Fisher lui répond. 





The slope of a tangent line 
20020304 

Ridley pose la question : Suppose a function f(x) has the line 3x+4y=2 as its tangent line at x=5. Find f'(5). Harley Weston lui répond. 





The tangent function 
20020112 

Justine pose la question : if you know that sin45degress = cos45degrees, how do you know that tan45degrees = 1? Penny Nom lui répond. 





A tangent line 
20011121 

A student pose la question : write an equation of the line tangent to the graph of
e^{y} + ln(xy) = 1 + e at (e,1) Harley Weston lui répond. 





A trig identity 
20010727 

Jeff pose la question : prove this identity and show steps tan(x/2+pi/4)=secx+tanx Harley Weston lui répond. 





Three tangents to a circle 
20010627 

Stephanie pose la question : The three lines PS, PT, and RQ are tangents to the circle. The points S, X, and T are the three points of tangency. Prove that the perimeter of triangle PQR is equal to 2PT. Chris Fisher lui répond. 





The normal to a curve 
20010408 

Varenne pose la question : I am having SO much trouble tackling this question and don't know what the right answer is... can you help me out? The question is
Find the equation of the normal to the curve y=(x2)^{2}/(1x)^{2} that is parallel to the line x+4y+7=0 Harley Weston lui répond. 





Common tangents 
20010408 

Anne pose la question : I have been working on this problem for a while but I'm not sure I'm getting the right answer: Find the common tangents of 2y=x^{2} and 2y=x^{2}16 Thanks for the help. :) Harley Weston` lui répond. 





The unit circle and trigonometry 
20010405 

Ashley pose la question : "My teacher wants us to find out what a unit circle is, which I found out, a circle with the radius of 1, but the problem is he wants us to show the relationship between the unit circle and the sine(30,45,60 degrees), cosine(30,45,60 degrees),and tangent ratios(30,45,60 degrees). I need help with this and my teacher will not help us out. Thanks very much ... Penny Nom lui répond. 





The angle of elevation 
20010308 

Jeffrey pose la question : At a Certain time, a vertical pole 3m tall cast a 4m shadow. What is the angle of elevation of the sun? Harley Weston lui répond. 





cot(arcsin 3/5) 
20010107 

Jason pose la question : Find value. Assume that all angles are in Quadrant 1. cot(arcsin 3/5) Harley Weston lui répond. 





Triangles and trigonometry 
20001130 

Mose pose la question : If I have a right triangle, and I know the lengths of all three sides, is there a formula that will allow me to determine the measurements of the 2 non right angles? Harley Weston lui répond. 





A trig question 
20000701 

Will pose la question : An open rectangular tank a units deep and b units wide holds water and is tilted so that the base BC makes an angle theta with the horizontal. When BC is returned to the horizontal, who that the depth of the water is (a squared) * cot theta div 2b units Harley Weston lui répond. 





Parallel tangents 
20000630 

Ebony Indalecio pose la question : I need to prove the theroem: Tangents to a circle at the end points of a diameter are parallel. Walter Whiteley lui répond. 





A parabola problem 
20000323 

Morin pose la question : I need to prove that if parabola x^{2}=4py has a chord (not necessarily a focal chord) intersecting it at points A and B, with tangents to the parabola at points A and B that intersect at C, then a line drawn through C and the midpoint of the chord M is parallel to the yaxis. Further, prove that the point D where this line intersects the parabola is the midpoint of line CM. Penny Nom lui répond. 





Angle of Intersection of Two Lines 
20000302 

Veronica Patterson pose la question : I am having a real hard time trying to figure out this problem. Could you please help me! The homework question says to find the acute angle of intersection between the two lines y=3x+1 and y=(1/2)x1. (It also says to use the results of a problem I had already figured out.) That problem was to use information from a picture shown that tan(theta sub1theta sub2)= ((m sub2 m sub1)/(1+(m sub1 * m sub2))). I used the difference identity of tangent to figure out the answer. Any help on this problem would be greatly appreciated. Harley Weston lui répond. 





Trigonometry history 
19980526 

Joeseph Huckler pose la question : Can you please tell me some history of the trigonometric ratio Tangent? who discovered it? when was it discovered and some other useful info... Penny Nom lui répond. 





The Length of a Chord. 
19970726 

Nathan Arthur pose la question : Picture a 9 inch diameter circle. Inside that circle is a 6 inch diameter circle tangent to it. Then, tangent to both circles is a 3 inch diameter circle. So there are three circles, two smaller ones inside a big one, all of them just touching but not overlapping. Now picture a chord on the 9 inch circle that is created by making a line that is tangent to both the 6 and the 3 inch circles and extending it to the edge of the 9 inch circle. I need the length of that cord. Chris Fisher lui répond. 





The angle between two tangents. 
19970609 

Felix Ho pose la question : Two tangents are drawn from the origin to the circle (x)(x)+(y)(y)4x6y+9=0. If the angle between the tangents is m, fine the value of tan(m). P.S. (x)(x)=square x Harley Weston lui répond. 





A trig problem 
19961213 

S. Johnson pose la question : sin t + cos t = 1/5. Find ALL exact values of cot t, given the original equation. Harley Weston lui répond. 





Height of a Hotel 
19961107 

Irene pose la question : "Irene" is to determine the # of floors in a hotel 500 feet up the street. Irene is on the 10th floor of an office building and can measure the angle of elevation to the top of the hotel, 57 degrees. Her view of the entire building is obstructed. If the street rises at an angle of 8 degrees from the office building to the hotel and the average distance between floors is 11 feet, how many floors are on the hotel? Penny Nom lui répond. 





A tangent to a circle is perpendicular to the radius at the point of contact. 
19961022 

Rita Leung pose la question : I wonder if there is any proof for this theorem  A tangent to a circle is perpendicular to the radius at the point of contact. If there is any proof for that, can you tell me please? Chris Fisher and Harley Weston lui répond. 

