







Two circles 
20190523 

Arman pose la question : Two concentric circles have their centres at
point C. The radius of the smaller circle is
8 cm. The length of chord AB is 26 cm and
is tangent to the smaller circle. What is the
circumference of the larger circle? 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. 





Two circles 
20170813 

Ladines pose la question : Find the equation of the circle passing through points of intersections of circles x²+y²=4y and x²+y²=2x and the center is on line y=2 Penny Nom lui répond. 





Two concentric circles 
20161221 

shrestha pose la question : Two concentric circles have radii of 14 cm and 7 cm respectively. Find the area of space between them. 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. 





Three circles 
20161030 

yolani pose la question : two equal circles with centre A (1;1)and B (4;5)touch a third circle with centre P as shown in the diagram. If P ,A and B Lie on a straight line find the coordinates of P Penny Nom lui répond. 





Two concentric circles 
20150528 

Shannan pose la question : Two concentric circles have radii of 24cm and 26cm. What is the length of the chord that is tangent to the inner circle? Include a sketch 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. 





The area of the ring between two concentric circles 
20150408 

Conner pose la question : The area of the ring between two concentric circles is 25pi/2 square inches. The length of a chord of the larger circle tangent to the smaller circle is? Robert Dawson lui répond. 





Two concentric circles 
20150225 

Manasi pose la question : The area between 2 concentric circles is 6 times the smaller circle. Radius of small circle is 7 cm. Find the difference in the circumference of the bigger circle ad the smaller circle? Penny Nom lui répond. 





Two concentric circles 
20150125 

nazneen pose la question : select the correct answer from the given four options
given are two concentric circles. radii of outer circle & inner circle are r1 & r2 respectively.
the areas of inner circle & shaded ring are equal. the radii r1 & r2 are related by?
1. r1 = r2
2. r1 = r2*square root 2
3. r1 = r2*square root 3
4. r1 = 2r2 Penny Nom lui répond. 





The region between two concentric circles 
20141027 

Ray pose la question : two circles, concentric; Given the length of chord of outer circle that is tangent to inner circle. what are the areas of both? how to calculate? Penny Nom lui répond. 





A circle is divided into three sectors 
20140417 

atolagbe pose la question : the area of a circle is 154cm square. it is divided into three sectors such that two of the sectors are equal in size and the third sector is three times the size of the other two put together. calculate the perimeter of the third sector. take pi=22/7? 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. 





2 concentric circles 
20131127 

Dimaris pose la question : The radius of the outer circle of 2 concentric circles is x. An
equilateral triangle inscribed in the outer circle also circumscribes the
inner circle. What is the radius of the inner circle in terms of x? Penny Nom lui répond. 





A string wrapped around three circles 
20131019 

Jim pose la question : A recent puzzle ' find the length of a string around 3 touching
1 meter diameter circles ' gave this answer : the string
touches 120° (or pi/3 meters) of each circle. Then
3(1+pi/3) = 3+pi meters is the required length. I do not see how
it was determined that the string touches 120° or pi/3 meters?
Please explain . Thankyou , Jim 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. 





Four circles 
20130529 

varsha pose la question : four circular cardboard pieces each of radius 7cm are placed in such a way that each piece touches two other pieces. find the area enclosed by the four pieces. Penny Nom lui répond. 





Two overlapping circles 
20130522 

Alexandra pose la question : There are two overlapping circles. The two nonoverlapping regions have areas A and B.
As the area of overlap changes, the values of A and B also change.
Prove that no matter how big and small the overlap is, the difference between
A and B is always the same. Penny Nom lui répond. 





Two congruent circles in a rectangle 
20121020 

Alexander pose la question : Have you ever solved a problem, in which you have a rectangle, from which you need to cut the largest two circles of equivalent diameter? I bisected a rectangle diagonally, but the circles, while tangent to two of the sides, are not tangent to eachother. Can you devise a method for two equivalent circles, that are tangent to two sides, are also to eachother?
Take for example a piece of paper, Each if the two largest circles has a diameter that is greater than the distance to the midpoint of the diagonal bisector of the rectangle. Chris Fisher lui répond. 





Two circle problems 
20121005 

shahad pose la question : question 1
find an equation for the circle through the point (0,0) and (6,0) that a tangent to the line y=1
question 2
find an equation for the circle through the point (0,0) and (17,7) whose center lies on the line 12x5y=0 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. 





The distance between overlapping circles 
20120726 

Jeff pose la question : I have two circles of different size that overlap one another:
Circle #1 has an area(A) of 731,475, so I can calculate its radius as 482.6.
Circle #2 has an area(A) of 502,517, so I can calculate its radius as 400.
If I know that the area where they overlap is 179,271, how can I calculate the distance between the midpoints of these two circles? Chris Fisher lui répond. 





A common chord to two circles 
20120422 

Nicole pose la question : What is a common chord between two circles and how is it found in the problem: Two circles intersect and have a common chord, the radii of the circles are 13 and 15, the distance between the circle's centers is 14, find the common chord. Penny Nom lui répond. 





Two overlapping circles 
20120321 

Monty pose la question : If you have a 3.75" radius circle overlapping a 5" radius circle with their centers 3" apart what would be the area of the nonoverlapped portion of the small circle? Penny Nom lui répond. 





Circles 
20120311 

Deniz pose la question : Two circles are externally tangent and the lengths of their diameters are 4 and 6. Find the length of the segment joining the centers of the circles. Penny Nom lui répond. 





Two circles 
20120208 

crisfe pose la question : find the point where the common cord of the circles x2+y2=25, x2+y212x6y+35=0 process there line centers. what point they intercepts? Penny Nom lui répond. 





A fountain 
20120124 

kris pose la question : A fountain has a radius of 14 meters to its outer edge. Their is an inner ring in the center of the fountain, where a statue of Sir Isaac Newton stands, that does not contain water. The inner ring has a diameter that is 6m less than the diameter of the outer ring of the fountain. What is the circumference of the inner ring? What is the area that is covered by water in the fountain? Penny Nom lui répond. 





Four pizzas 
20120123 

kris pose la question : a pizza company wishes to put 4 medium pizzas in a box to sell as a party pack. The box they want to use the square and has dimensions of 60cm by 60cm. They need you to help them calculate the dimensions of the pizza that will fit in the box. Calculate the following: area, radius, diameter, circumference Penny Nom 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. 





Two circles 
20111204 

Luke pose la question : Two fixed circles intersect at A and B.
P is a variable point on one circle.
PA and PB when produced meet the other circle at M and N respectively.
Prove that MN is of constant length.
Thanks!
p.s. I also sent the question with a figure via email. Chris Fisher 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. 





Two great circles 
20111006 

Jean pose la question : "Two great circles lying in planes that are perpendicular to each
other are drawn on a wooden sphere of radius "a". Part of the sphere
is then shaved off in such a way that each cross section of the
remaining solid that is perpendicular to the common diameter of the
two great circles is a square whose vertices lie on these circles.
Find the volume of this solid."
I don't understand the geometry of the problem.
Can you please explain the problem and if possible draw a diagram for me
? 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. 





concentric circles 
20110706 

maribiie pose la question : two circles are concentric. the tangent to the inner circle forms a chord of 12cm in the larger circle. find the area of the "ring" between the two circles? 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. 





Semicircles and the Pythagorean Theorem 
20110109 

Jas pose la question : Okay well, in math we are learning about the pythagorean theorem and we have to do a math journal on the question:
****Can you replace the squares (that are put on the sides of a right triangle) with semicircles and still get the same answer??
I do not understand because i tried doing an example and comparing it with a normal way of doing it and I didnt get the same answer! Penny Nom lui répond. 





Two overlapping circles 
20100804 

Husen pose la question : two circles of radius 5 cm intersect each other .the distance between their centers is 5root 2.find the area of the portion common to the two circles Penny Nom lui répond. 





Four circles in a square 
20100604 

Daniela pose la question : four circles are drawn in a square such that the circles are tangent to each other as shown. find the area of the shaded region. It the goes on to show a diagram with a square and four circles drawn in it. The length of a side of the square is 24. Please help me! Penny Nom lui répond. 





A circle inscribed in a square inscribed in a circle 
20100428 

jouniella pose la question : A square is inscribe to the first circle, then another circle is inscribe to the square. Find the ratio of the 2 circles. Penny Nom lui répond. 





Two overlapping circles 
20100412 

Scott pose la question : There are two circles, big circle with radius R and small one with radius r. They intersect and overlap in such a way that the common area formed is 1/2 pi r^2 (half the area of the small circle). The Question is: suppose we have known the radius r of the small circle, and the distance between the two circle centers, what should the radius R of the large circle be? Chris Fisher lui répond. 





Two overlapping circles 
20100307 

Hayden pose la question : I have two circles of equal size. The radiuses of the circles are 30ft. The two circles are positioned 40ft apart and I need to find the area where they overlap. Harley Weston and Tyler Wood lui répond. 





Two overlapping circles 
20091119 

Raraa pose la question : There are two identical circles . The edge of one circle is at the middle point of the other circle. There were overlapped . The area of the overlapped surface is 20000 square centimetres . How do I find the radius of the circle rounded to the nearest whole centimetre ? Penny Nom lui répond. 





Concentric circles 
20091014 

maddy pose la question : Find the exact area of the region bounded by two concentric circles with radii 10 inches and 6 inches. Penny Nom 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. 





Seven circles 
20090920 

Bobbi pose la question : try to put number 1 to 7 in seven circles (one in the middle, 3 on top, 3 below) so the numbers in each row of three circlesvertical, horizontal, and diagonal  add up to 12. Each number can be used only once. Stephen La Rocque lui répond. 





Two circles 
20090803 

Karan pose la question : We are given 2 circles with radii 12cm and 3 cm. We have to find AB Penny Nom lui répond. 





Two circles on a dome 
20090701 

Beth pose la question : My question is related to a dome I would like to construct, for which I know the circumference of the base: 120ft.
I now need to figure out the diameters of two smaller circles, one at 20ft along the arc of the dome form the ground,
and the other at 30ft along the arc.
Assuming a true hemisphere, or 180 degrees total arc, how can I calculate these two circumferences?
Beth Stephen La Rocque 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. 





Three circles inscribed in a circle 
20081218 

seema pose la question : three equal circles each of radius 1 cm are circumscribed by a larger circle.find the perimeter
of circumscribing circle? Robert Dawson 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. 





Four circles in a square 
20081119 

Anthony pose la question : I have a square where one side measures 10cm and within that square
There are four equal quarter circles. Each quarter circles starts in a
different corner of the square and I am trying to find area inside the
overlap on the quarter circles. Janice Cotcher, Chris Fisher and Penny Nom lui répond. 





The region between two circles 
20080924 

Carol pose la question : Good day!
Here is a picture of the problem that we need to solve. (I send the picture through email.)
A small circle is inside a larger circle, the only given in the problem is the chord of the larger circle tangent to the smaller circle which measures 16cm. The question is, what is the area of the shaded region?
Can you answer this question? Thanks! :) Harley Weston 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. 





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. 





Two circles 
20080610 

cey pose la question : the diameter of the larger circle is 20cm, and the smaller 10cm. what is the shaded area?? Janice Cotcher 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. 





Two overlapping circles 
20080426 

Michelle pose la question : Two overlapping circles O and Q have the common chord AB (vertical line between the overlapping circles). If AB is 6 and circle O has a radius of length 4 (horizontal line going through the overlapping circles and touching the side of the circle) and circle Q has a radius of length 6, how long is OQ. Penny Nom and Walter Whiteley lui répond. 





Two intersecting circles 
20080417 

Muhammad pose la question : Hi, how can we find the perimeter and area of the region common to two intersecting circles of radii 6 cm and 4 cm with centers 7 cm apart. 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 common chord to two circles 
20080309 

shubha pose la question : please help me out with this problem.
find the length of the common chord of the intersecting circles x2+y24x5=0
and x2+y22x+8y+9=0 Stephen La Rocque lui répond. 





Two circles and a triangle 
20080307 

Adrian pose la question : The vertices of a rightangled triangle are on a circle of radius R and the
sides of the triangle are tangent to another circle of radius r. If the lengths
of the sides about the right angle are 16 and 30, determine the value of
R+r Penny Nom lui répond. 





Two circles in a rectangle 
20080118 

Alex pose la question : One side of a rectangle is 10 and the other is x.
Two circles with equal radii are inscribed in the rectangle and like a Venn Diagram, the circles overlap.
Each circle touches the top and bottom of the rectangle and the left circle touches the left side of the rectangle and the right circle touches the right side of the triangle.
The distance between the centre of each circle is 2x/3.
Find x Penny Nom lui répond. 





Seven circles in a circle 
20080110 

fae pose la question : what is the area of the remaining portion of a large circle with radius 12cm and the seven smaller and equal circles just fit inside? Penny Nom lui répond. 





Great circles 
20071105 

Lindsay pose la question : Does a sphere have only ONE great circle? Explain? Stephen La Rocque lui répond. 





Three circles 
20070929 

Kevin pose la question : 3 given circles of R80, R56 & R24 are all in contact. The 2 smaller ones are inscribed in the big one.
Find by calculation or graphically (both if possible) the radiusof a 3rd circle which will be in contact with all 3 given circles. 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. 





A sequence of circles 
20070611 

Ann pose la question : Please help with solving the following problem!!!
A circle is inscribed in an equilateral triangle with a side of length 2.
Three circles are drawn externally tangent to this circle and internally
tangent to 2 sides of the triangle. 3 more circles are drawn externally
tantgent to these circles and internally tangent to 2 sides of the triangle. if
this process continued forever, what would be the sum of the areas of all the
circle? the answer 1 parent came up with was Pie over 2, but we don't
know how he did it. Can you please show the work or explain the answer to
this problem?
Thank you
Ann
p s my daughter is in 9th grade math. Steve La Rocque, Chris Fisher and Penny Nom lui répond. 





Two concentric circles form an annulus 
20070502 

A student pose la question : In the diagram below, two concentric circles form an annulus. The
vertical line is tangent to the inner circle, and forms the diameter of
a third circle.
Explain why the areas of the annulus and third circle are the same. Penny Nom lui répond. 





A square contains five circles with the same radius. 
20070421 

Jamie pose la question : A square has a side length on 1 m.
The square contains five circles with the same radius.
The centre of one circle is at the centre of the square and it touches the other four circles.
Each of the other four circles touches two sides of the square and the center circle.
Find the radius. Penny Nom lui répond. 





Two concentric circles 
20070419 

James pose la question : Two concentric circles have a chord running through the outer one. The chord is the tangent of the inner circle and is 14 cm.The outer circle is shaded and the inner circle is not. Find the exact area of the shaded region without using a calculator. Stephen La Rocque lui répond. 





Four semicircles are drawn inside a square 
20070419 

James pose la question : Four semicircles are drawn inside a square, with the diameter being the length of the square.The overlapping portion of the semicircles are shaded. What fraction is shaded? Penny Nom lui répond. 





Area of circles within a circle 
20070408 

Avaline pose la question : Imagine that there are four small circles inscribed in a bigger circle. The 4 small circles are shaded. What is the ratio of the area of the shaded region to the area of the unshaded region? Stephen La Rocque lui répond. 





circles 
20070306 

chetna pose la question : A large circle has a radius of 10cm.Given four congruent circles tangent to one another within the large circle what is the radius of the largest circle which will fit in the middle ? Stephen La Rocque lui répond. 





Circles 
20070222 

Erika pose la question : I have a research paper due on real life uses of conic sections I've looked through all your conic topics and uses of them, but and i cant seem to find real life uses for circles. What are real life uses of circles? Penny Nom lui répond. 





Two concentric circles 
20070211 

maria pose la question : i have a problem with this quadratic word problem which i am trying to solve it but couldn,t get it please help me to solve this question Two concentric circles are drawn, the radius of one being 2cm greater than that of the other. The area of the ring enclosed between the two circles is one quarter of the area of the smaller circle.Calculate the radii of the circles,correct to three significant figures. (Don,t substitute for pie) Stephen La Rocque lui répond. 





Circles and polygons 
20061211 

Irene pose la question : Can you define a circle as a polygon with an infinite number of sides which are infinitely small? If you can, can you then define a cylinder as a prism? The sides would be rectangles or parallelograms with one length infinitely small? Chris Fisher lui répond. 





Sectors of a circle 
20061130 

Maithreyi pose la question : A circle of diameter 21m is divided into three sectors with central angles 60degree,120degree and 180degree. Find the area of each sector? Stephen La Rocque lui répond. 





Conic sections 
20061119 

Joyce pose la question : My son has a project on conic sections. I need the following information on Parabola, Circle, ellipse,and hyperbola. He can't find the following information for each conic section: equations with explanations, four uses for each shape and Shape explanation. Penny Nom lui répond. 





An equilateral triangle has been wedged in between two circles. 
20060922 

Kim pose la question :
An equilateral triangle has been wedged in between two circles. How does the diameter of the smaller circle compare to the diameter of the larger circle.
image: circle inside of an equilateral triangle touching all sides of the triangle; both the triangle and the circle inside are placed into a larger circle where the triangle vertices all touch the circle
Penny Nom lui répond. 





Three circles inside a larger circle 
20060416 

Meghan pose la question : Given three congruent circles tangent to one another (radii = 1), what is the radius of a circle circumscribed around them?
Stephen La Rocque lui répond. 





Overlapping area of two circles 
20060415 

Jade pose la question : Given two identical circles where the radius (6 units) is the distance between the centers, what is the area of the overlapping region?
Stephen La Rocque lui répond. 





An epicycloid 
20060410 

Sharon pose la question : What is the name of the curve formed by a point on the circumference of a circle that rolls on the outside of a fixed circle? This curve is used in the study of gears. Stephen La Rocque and Penny Nom 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. 





Make 2 rows of 4 circles with only 6 circles 
20060131 

Sarah pose la question : Moving as many circles as you need, make 2 rows of 4 circles only having 6 circles? Chris Fisher lui répond. 





Sectors and arcs 
20060125 

Wael pose la question : How is the area of an arc (alpha*pi*r squared/360) derived?
How is the length of an arc (alpha*pi*r/180) derived? Penny Nom 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. 





Framing an arched wall 
20050812 

Mike pose la question : I'm framing a building wall with a curved (arcing) top section. The radius of the section is 74'6" with a height above finish floor of 16'0". The horizontal run of the arced section is 23' 1 1/2" with a low height above finish floor of 12'4". If I start with a 16' stud at the high end how long are the subsequent studs if they are on 16" centers? Short of laying this out on a tennis court how can I work out the lengths of the studs? Penny Nom lui répond. 





Two overlapping circles 
20050320 

Safi pose la question : I have a problem to calculate the area of two overlapping circles because two circles are overlap then how i calculate the overlap area to subtract from the area of both circle. 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. 





Arcs and chords 
20050109 

Aniesha pose la question : A chord of a circle is 48 centimeters long and is 10 centimeters from the center of the circle. Find the radius? Penny Nom lui répond. 





Irrigation and a sector of a circle 
20041223 

Chuck pose la question : A friend of mine is a farmer and uses Pivots to irrigate portions of his land. The crop rows are in straight lines that all form chords of a large circle. The intent is to determine area between any two "boundary" rows expressed in acres. Harley Weston lui répond. 





A regular hexagon is inscribed in a circle. 
20041208 

Abraham pose la question : A regular hexagon is inscribed in a circle. What is the ratio of the length of a side of the hexagon to the minor arc that it intercepts?
(1) pi/6
(2) 3/6
(3) 3/pi (This is the correct answer.)
(4) 6/pi
I found the length of the minor arc to be (pi)(r)/3 by doing a sixth of the circumference(2pi r).But I can't find the length of the radius to finish off the problem. If I knew the radius I would then plug it into the above and then use the radius again to be the length of the side because the triangle(one of the six of a hexagon) is equilateral. But can you show me how to get the radius to be 3? Thank you so much.
Walter Whiteley lui répond. 





A belt around two pulleys 
20041207 

Ian pose la question : a belt is stretched around two pulleys whose centers are d units apart and whose radii are R and r respectively (obviously R+r<d). the challenge is to find the length of the belt, l as a formula in terms of R, r, and d only. Penny Nom lui répond. 





An arc of a circle 
20041205 

Ruben pose la question : i have an arc 55 inches wide, 12 inches high at the centerline of the arc. how can i determine the diameter of the circle that would correspond to the arc. Penny Nom lui répond. 





Circles in a hexagon 
20040411 

Crystal pose la question : step by step can you show me how to calculate the area of the region inside the hexagon but outside the seven circles. given the radius of each circle is one inch 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. 





Definitions and descriptions 
20030608 

Tammy pose la question : MY DAUGHTERS TEACHER ASKED HER TO GIVE BOTH A DESCRIPTION AND A DEFINITION OF THE FOLLOWING ... CIRCLE, SQUARE, TRIANGLE,HEXAGON...... THE LIST GOES ON. WHAT IS THE DIFFERENCE BETWEEN DEFINITION AND DESCRIPTION ? DO A CIRCLE FOR AN EXAMPLE PLEASE. 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. 





I have three circles... 
20030130 

Tony pose la question : I HAVE THREE CIRCLE THAT IS CIRCLE TOGETHER: IN CIRCLE A, THE NUMBERS ARE: 11 I KNOW IS IN CIRCLE A, BUT I HAVE THE: 5 THAT IN A AND C, I HAVE THE 2 IN THE CIRCLE C AND B AND AND A, THE CIRCLE C I KNOW THAT 10 IS IN THE CIRCLE THE 4 IN CIRCLE A: AND B: IN CIRCLE B, I KNOW NUMBER 13 IS IN CIRCLE B; BUT I HAVE THE 3 IN CIRCLE B AND C AND I HAVE THE 2 IN CIRCLE B AND C AND A ,THE 4 IN CIRCLE B AND A. HOW DO I FIND THE SUM IN CIRCLE C AND IN B IN BOTH CIRCLE A AND B AND B AND C NOT IN CIRCLE B, AND NOT CIRCLE C. 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. 





Subdividing a circle 
20021111 

David pose la question : Say you have a cirlcle. Then you draw 2 dots on the circle. Then you connect the dots with lines. The circle is divided into 2 parts. If you do the same with 3 dots and connect each dot to each dot with a line then you get a circle with 4 parts. 4 dots with lines connecting all (6 lines) = 8 parts.... Claude Tardif lui répond. 





A Circle is evenly divided into six equal triangles 
20020916 

Marilynn pose la question : A Circle is evenly divided into six equal triangles leaving an area between the outside of the circle and the one side of the triangle. This area is measured as 3.14. What is the length of the radius, one line on the triangle? Paul Betts lui répond. 





The circumference of a 72 
20020814 

Linda pose la question : What is the circumference of a 72" diameter circle? Penny Nom lui répond. 





Overlapping circles 
20020529 

Naman pose la question : There are two circles, big circle with radius R and small one with radius r. They intersect and overlap in such a way that the common area formed is 1/2 pi r^{ 2} (half the area of the small circle) If r=1, find the Radius of the big circle (R)? Harley Weston lui répond. 





Chord length 
20020517 

Ashlie pose la question : How do you find the chord length of one section of a chord if you only have the diameter length and the other whole chord length. WV is the diameter and equals 16. XY is perpendicular to it, and equals 10. They intersect at pt. Z. I need to know what WZ equals. Please help! Penny Nom lui répond. 





Three chords 
20010628 

Paul pose la question : AE is a diameter of a circle and AC, CD and DE are chords of lengths 1, 2 and 3 respectively. (See the diagram.) Find the ridius of the circle. 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. 





Circles, ellipses, parabolas and hyperbolas 
20010509 

Colleen pose la question : How is an ellipse like a circle? In what way does an ellipse have a center? How is a hyperbola similar and different to an ellipse? How is a parabola similar a different to a circle ellipse and parabola? Pnny Nom lui répond. 





A quartercircle and two semicircles 
20001231 

Christopher pose la question : Inside the quartercircle are two semicircles with the same radius, (r). Which has a greater area, G or L? Penny Nom lui répond. 





Grazing area for a goat 
20000310 

Amy pose la question : A goat is tied in the middle of a side of a square building whose sides are 2 yards long. The rope is 4 yards long. What is the grazing area for the goat? Harley Weston lui répond. 





Rolling Circles 
19990912 

Craig Ellis pose la question : We have a circle of radius 3. inside the circle and tangent to the circle of radius 3 at one point is a circleof radius 1. The question is if we could roll the smaller circle around the inside of the larger circle how many revolutions would it take to get around to where we started. Chris Fisher and Walter Whiteley lui répond. 





Circles, cirmcuference and area 
19990516 

Stephen Ehrler pose la question : I would appreciate if you could please tell me if what I discovered here is something or my ignorance? I noticed that a circle with r radii has the folling characteristic. r = [2 * ( pi * r^{2} / pi * 2r)] The equation states that the ratio of a circles area over its circumfrence = 1/2 that of the circles radii. It works every time. Did you know this ? Is it some kind of therom and can it be used for any thing? I thought this was intresting and would appreciate any input you may have. Thank you. Chris Fisher lui répond. 





Circles 
19990421 

Alex Elkins pose la question : How do you find the circumference of a circle if you only know the radius and the square feet or inches of the circle if the radius is 18 inches, If done in inches do you multiply by 12 to get the square feet? Jack Lesage and Harley Weston lui répond. 





Two Inscribed Trapezoids 
19980127 

James pose la question : A hexagon inscribed in a circle has three consecutive sides each of length 3 and three consecutive sides each of length 5. The chord of the circle that divides the hexagon into two trapezoids, one with three sides each of length 3 and the other with three sides each of length 5, has length equal to m/n, where m and n are relatively prime positive integers. Find m+n. Haragauri Gupta lui répond. 





A geometry problem 
19971120 

Herman pose la question : When produced, two equal chords AB and CD of a circle meet at P in an angle of 24 degrees. If H is the midpoint of AB and K is the midpoint of CD, calculate the size of angle HKD. 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. 





Area Between Two Sectors 
19970302 

Rebecca Henry pose la question : Points A,B,C,D,E,F are equally spaced on a unit circle. Arc CGE has a center A. Find the number of square units of area in the shaded region. Walter Whiteley lui répond. 





Some Circle Questions. 
19970225 

Staci Vawser pose la question : A circle with a radius of 10m is drawn. A chord is drawn across the circle. How is the area that is formed between the chord and the arc calculated? Harley Weston lui répond. 

