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Browse High School Conic Sections, Circles
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
About ellipses.
Find the center of a circle.
Is a circle a polygon?
Volume of a tank.
Why is a circle 360 degrees?
 Perimeter of an Oval [04/08/1999]

What is the perimeter of an oval called?
 Perimeter of a Right Triangle [08/14/2001]

What is the perimeter of a right triangle with hypotenuse 65 that can be
circumscribed about a circle with radius 12?
 Placing Coins That Touch [8/7/1996]

How many 20cent coins can you put around a 20cent coin so that all of
them touch?
 Point in a Circle [04/29/1997]

Given a circle with two 6inch chords running across the top and the
bottom... find the probability that a point chosen at random is in the
region between the chords.
 Point on an Ellipse [05/16/1997]

Given an ellipse and an arbitrary angle theta from either axis, how do
you find the coordinates of the intersection of the ellipse and a vector
formed by angle theta?
 Points within an Ellipse [06/03/2003]

How to generate points that will be within an ellipse.
 Polygons, Infinite Sides, and Circles [04/03/1997]

Can a regular polygon with an infinite number of sides be a circle?
 Probability That Random Chord Exceeds Radius in a Circle [11/20/2004]

If a chord is selected at random on a fixed circle, what is the
probability that its length exceeds the radius of the circle?
 Product of Radii of Two Circles [7/22/1996]

The length of a common internal tangent to two circles is 7, and a common
external tangent is 11...
 Product of the radii [7/3/1996]

The length of a common internal tangent to two circles is 7, and a common
external tangent is 11...
 Proof of the Feuerbach Theorem [03/14/2000]

Please submit the proof of the Feuerbach theorem (the ninepoint circle
is tangent to the incircle and the circumcircle of a triangle.)
 A Proof using Analytic Geometry [02/24/1999]

Prove that, if p is a point inside the ellipse, there is one and only one
chord QP bisected at P.
 Putting a Ribbon around the Earth [12/23/2006]

I've heard that if you have a ribbon wrapped around the equator of the
earth, and you want to increase its length so that it floats 1" above
the earth all the way around, you only need to add 6.28" to the
ribbon. Is that really true? How is it possible?
 Quadrilaterals and Inscribed Circle [05/06/1999]

From ten sticks of lengths 1,2,3,....,10 four are selected to form the
sides of a quadrilateral...
 Radius and Center of a Circle from 3 Points [07/23/1999]

Given the coordinates of three points on a circle, how can you find the
center and radius?
 Radius, Center of Circle Given 3 Points [8/28/1996]

What is an easy formula to calculate the center point and radius of a
circle given three points on the circumference?
 Radius from an Arc and a Chord [06/08/1999]

If I know the height of an arc from the midpoint on a chord, and the
length of the chord, can I find the radius of the circle of which the arc
is a part?
 Radius of a Circle Inscribed in a Triangle [06/02/1999]

What is the radius of an inscribed circle of a triangle with sides 3, 4,
and 5?
 Radius of an Arch [05/25/1998]

Is there a formula to calculate the radius of a circle given the chord
length and the distance from the centre of the chord to the circle?
 Radius of a Racing Circle [09/20/1999]

How can I find the equation for the radius of a 'racing circle' (the
fastest path a racecar can take through the corner defined by the
quadrants of two circles), an arc sandwiched between identical quadrants
of two concentric circles?
 Radius of Circumscribed Circle [05/11/2001]

Where can I find a derivation of R = abc/4K?
 Radius of Curvature [07/23/2003]

I have several ellipses whose major and minor diameters I know, but
I have no information about their foci.
 Rail Bend in Hot Weather [10/13/2002]

A 20ft piece of rail expands 1 in. in length during a hot spell. If
there are no expansion gaps, how high off the ground will the rail
rise?
 Railroad Track Expansion [04/07/2003]

A continuous straight railroad track of one mile is permanently tied
down at both ends. As the day heats up, the coefficient of expansion
of steel causes the rail to expand so that the length is now 5281
feet. Assuming that the track expands upward, what maximum vertical
distance from the horizontal will the track rise at the highest point?
 Ratios, Geometry, Trigonometry [06/10/1999]

A homeschool teacher asks for help with triangles, flagpoles, and
circles.
 Rectangular Hyperbola [06/11/2002]

The graph of a rectangular hyperbola looks nothing like a rectangle.
Where does the name come from?
 Reflection Points on a CircleShaped Mirror [09/30/2003]

Points A and B are located within a circle. If A were a light emitting
point and B a light receiving point, then B would receive light from
points P on the circle. How can I find these points?
 Reflections in Parabolic Mirrors [05/14/2005]

I know that in a parbola, any ray that starts at the focus and hits
the parabola is reflected parallel to the central axis of the
parabola. Can you explain or prove why that happens?
 Reflective Properties of a Semicircular Mirror [05/16/2000]

What are the reflective properties of a semicircular mirror? Will a ray
exit a semicircular mirror parallel to its entry line?
 Relationship between Circumference and Area [11/08/2007]

My 6th grade daughter asked if there is a shortcut for converting from
area to circumference and back without finding the radius.
 Rhumb Lines and Great Circle Routes [09/24/1998]

Can you explain great circles and rhumb lines and how they relate to
shortest distances in geometry?
 Right Triangle Inscribed in a Parabola [09/20/1999]

Show that the point of intersection Q of the axis of the parabola y=x^ 2
and the hypotenuse of right triangle RST (inscribed in the parabola so
that R coincides with the vertex of the parabola) is independent of the
choice of right triangle.
 Rounding Pi [06/01/1999]

Can you prove that the value of Pi cannot be rounded down to 3.0? Is there an error in the Bible?
 SecantTangent Theorem [03/21/2002]

I'm trying to prove the secanttangent theorem.
 Semicircle Proof [02/27/2001]

M is the midpoint of AB. Three semicircles with diameters AM, MB, and AB
are drawn. A circle with centre O and radius r touches all three. Prove
that r = 1/6 AB.
 Shared Points on Concentric Circles [03/11/2004]

Can two concentric circles share only a few points? If they are
concentric and they have the same radius, they would share all of
their points, and if they don't have the same radius they will share
no points. It seems like it's all or none.
 Simplifying Circle Formulas from the Dr. Math FAQ [04/30/2004]

In your FAQ on circle formulas, in the sections where the other five
values are derived from any two known values, could you write each
formula in terms of only the two known values, instead of using the
intermediate steps?
 Simson Line [04/19/1999]

What is the Simson line?
 Simson Lines [06/07/2001]

Show that, given two triangles inscribed in the same circle, for any
point P on the circle the two Simson's lines form a fixed angle.
 Slicing Up a Circle [03/22/2001]

Find a formula that will give the maximum number of pieces with n number
of straight slices of the circle.
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