







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 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. 





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. 





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 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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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 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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 

