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A circle is inscribed in a hexagon 2015-12-28
From Lalitesh:
A circle is inscribed in a regular hexagon ABCDEF
Prove that AB+CD+EF=BC+DE+FA

Answered by Penny Nom.
A common tangent to two general parabolas 2015-11-15
From Kind:
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.

Answered by Chris Fisher.
Two concentric circles 2015-04-21
From Juniper:
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?
Answered by Penny Nom.
Two parallel tangents to a circle 2015-03-05
From Samantha:
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.
Answered by Penny Nom.
A triangle and an incircle 2013-05-09
From Max:
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.

Answered by Chris Fisher.
Lines tangent to y^2=4x 2011-11-11
From Reuchen:
Find equations of the lines tangent to y^2=4x and containing (-2,1).
Answered by Penny Nom.
A family of circles 2011-03-01
From steffi:
Find the equation of the family of the circle passing through the the point of intersection of x^2+ y^2 -4x-28=0 and x^2 +y^2 -4x-20+52=0; the member tangent to x=7.
Answered by Penny Nom.
A cyclic quadrilateral 2009-01-23
From Murtaza:
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.
Answered by Robert Dawson and Chris Fisher.
Two tangent circles and common tangents 2008-12-01
From Alan:
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
Answered by Penny.
Two tangents to a circle 2008-11-26
From rogerson:
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?
Answered by Penny Nom.
Two tangent lines to a parabola 2008-10-26
From Marcus:
Show that the tangent lines to the parabola y = ax^2 + bx + c at any two points with x-coordinates p and q must intersect at a point whose x-coordinate is halfway between p and q.
Answered by Penny Nom.
How many parallel tangents may a circle have? 2008-09-29
From Manish:
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..
Answered by Walter Whiteley.
How many bricks I can place around a 26-inch circle? 2008-05-22
From Jon:
I want to know how many bricks I can place around a 26-inch circle? There must be a formula other than trial and error. The length of the bricks is 6-inches. [How many 6-inch tangents can be in a 26-inch circle? Thank you very much. Jon
Answered by Harley Weston.
Tangents to a circle 2007-08-18
From Laura:
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.
Answered by Chris Fisher.
Two tangents to a circle 2007-04-17
From Doug:
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.
Answered by Stephen La Rocque.
Tangent lines 2006-11-09
From Melissa:
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?

Answered by Stephen La Rocque.
A sequence of circles and tangents 2006-01-16
From Paul:
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)).
Answered by Chris Fisher.
Two tangents to a circle 2005-06-18
From Tej:
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.
Answered by Penny Nom.
A geometry problem 2004-03-04
From Jennifer:
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
Answered by Chris Fisher.
A theorem in geometry 2003-09-02
From Diego:
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 PT2 = AP x BP.
Answered by Dieter Ruoff and Penny Nom.
Constructing a tangent to two circles 2002-11-28
From Tom:
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?
Answered by Chris Fisher and Penny Nom.
Three tangents to a circle 2001-06-27
From Stephanie:
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.
Answered by Chris Fisher.
Common tangents 2001-04-08
From Anne:
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=x2 and 2y=-x2-16 Thanks for the help. :)
Answered by Harley Weston`.
Parallel tangents 2000-06-30
From Ebony Indalecio:
I need to prove the theroem: Tangents to a circle at the end points of a diameter are parallel.
Answered by Walter Whiteley.
A parabola problem 2000-03-23
From Morin:
I need to prove that if parabola x2=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 y-axis. Further, prove that the point D where this line intersects the parabola is the midpoint of line CM.
Answered by Penny Nom.
The Length of a Chord. 1997-07-26
From Nathan Arthur:
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.
Answered by Chris Fisher.

The angle between two tangents. 1997-06-09
From Felix Ho:
Two tangents are drawn from the origin to the circle (x)(x)+(y)(y)-4x-6y+9=0. If the angle between the tangents is m, fine the value of tan(m).

P.S. (x)(x)=square x
Answered by Harley Weston.




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