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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?
 Finding the Center of a Circle from Three Points [05/22/2000]

How can I find the coordinates of the center of a circle, given the
coordinates of three points on its circumference?
 Finding the Center of a Circle Given 3 Points [05/25/2000]

How can I find the coordinates of the center of a circle given the x and
y coordinates of 3 points that lie on its circumference?
 Finding the Center of a Disk [12/13/2002]

I need to find the center of a solid disk to bore a hole.
 Finding the Circumcenter of a Sphere [09/24/2003]

How can I find the circumcenter of a sphere given 3 points on the
sphere, along with the radius?
 Finding the Circumference of a Circle Using Its Shadow [1/26/1996]

I am attempting to find the circumference of a large sphere that is
hanging 25 feet in the air.
 Finding the Intersection of Two Circles [08/19/1999]

How can I find the intersection points of two circles?
 Finding the Radius and Center of a Circle [06/19/2002]

How do I find the center and radius for the circle defined by the
equation x^2 + 8x + y^2  6y = 11?
 Finding the Radius of a Pipe [1/28/1996]

A pipe has become bent and is no longer round. In order for me to correct
the problem, I must build a brace to go around the pipe and true it up.
However, until I can determine the radius of the pipe, a brace cannot be
built.
 Finding the Table's Diameter [05/05/2001]

A circular table is pushed into the corner of a room so that it touches
both walls. On the edge of the table is a scratch 8" from one wall and 9"
from the other wall. What is the diameter of the table?
 Find the Center of a Circle Using Compass and Straightedge [10/15/2003]

How can I find the center of a circle?
 Fitting a Circle to a Given Set of Points [08/12/2005]

Given a set of points how do you calculate the circle of best fit?
 Fitting a Circle to Three Given Points [02/19/2006]

How can I use a system of equations to find the equation of a circle
that passes through three given points?
 Five Noncollinear Points [4/2/1995]

In general, how many undirected lines and how many circles are
determined by five noncollinear points?
 Flattened Cone [08/30/1998]

Drawing a shape you could cut out and roll up to form a cone whose crosssection you are given.
 Foci of an Ellipse [06/08/2001]

If the major and minor axis of an ellipse are given, how do I find the
focus points?
 Folding a Circle to Get an Ellipse [01/08/2001]

How can I prove that taking a point on a circle, folding it to an
interior point, and repeating this process creates an envelope of folds
that forms an ellipse?
 Formation of a Cone [03/16/2003]

Why is a cone formed when a sector is removed from a circle and the
edges of the remaining segment joined?
 Formula for Common Tangents [5/27/1996]

What's a simple formula that will define the common tangent of two
circles of different diameters?
 Formula for the Circumference of an Ellipse [6/27/1996]

What is the formula for the circumference of an ellipse?
 Formula for the Length of a Chord [7/3/1996]

What is the formula for the length of a chord given either the circle
radius or the area of the resulting circle segment?
 Formula to Calculate Overlap of Two Arcs on a Circle [05/27/2005]

I have a circle and I draw an arc from 0 to 45 degrees with a blue
pen, and another from 40 to 60 degrees with a red pen. Now I know that
the arcs are intersecting from 40 to 45, but I want to construct a
formula with the 4 angle entries and one output for the intersection
answer.
 Geometric Proof of Heron's Formula [01/25/2000]

How can I prove Hero(n)'s formula using a circle with center P and radius
R inscribed in triangle ABC?
 Geometry: Minimum Distances and Circles [11/3/1994]

Given an arbitrary circle with two arbitrary points A and B within it,
using compass and ruler only, is there a way to find a point C on
the circle such that the sum of the length AB and the length BC is a
minimum?
 Geometry of a Circle (Arcs and Angles) [10/13/1997]

DE is a diameter of circle O, and is perpendicular to chord AB at point
C...
 Geometry Proof Involving Circle and Triangle [09/26/2005]

Triangle ABC cuts a circle at points E, E', D, D', F amd F'. Prove
that if AD, BF and CE are concurrent, than AD', BF' and CE' are also
concurrent.
 Graphing a Circle from the General Equation [05/20/2004]

How do you graph x^2 + y^2 = 25? I know it's a circle, but I don't
know how to graph it.
 Graphing an Ellipse [11/20/1998]

How do you graph an ellipse? What is the equation?
 Grazing Areas [05/29/2001]

Find the total area grazed by three horses.
 A Hexagon Inscribed within a Circle [2/29/1996]

A hexagon is inscribed within a circle. Three consecutive sides have a
length of 3 and the other three consecutive sides have a length of 5. A
chord is drawn within the circle....
 History of Circle Area Formula [03/19/2007]

Do we know who figured out that pi*r^2 gives the area of a circle?
 How Did Eratosthenes Measure the Circumference of the Earth? [6/26/1996]

Didn't Eratosthenes measure the lengths of shadows of sticks at different
locations on the same day and time of the year, so he had two right
triangles...?
 How Many Edges in a Circle? [06/15/1999]

Are there one, none, or an infinite number of edges in a circle?
 How Many Points Determine a Parabola? [12/20/2000]

How can we determine whether or not a given plane curve is a parabola?
Under what conditions is a parabola uniquely determined?
 Importance of Reasonable Approximation [08/07/1999]

A stairway profile, and the calculation of arc length and curved surface
area.
 Incenter and Conway's Circle [12/17/2002]

In a triangle, the bisectors of the angles intersect at a point in
the interior of the circle. If I use this point as a center to draw a
circle, what is the relation of this circle to the triangle?
 Incircles Tangent to a Common Line [03/23/2001]

In triangle ABC, the incircle touches side AB at M. T is an arbitrary
point on BC. How can I show that the incircles of triangles BMT, AMT and
ATC are all tangent to a common line?
 Incribing a Pentagon in a Circle [2/6/1996]

I'm stuck trying to inscribe a pentagon. I can easily inscribe a square
by just drawing two perpendicular diagonals. I also know that 360/5 = 72
but that doesn't help me at all. Can you help?
 Inscribed Angle, Circle Equation [6/14/1996]

What's an inscribed angle? What's the equation for a circle with a center
at (8,1) and a radius of 15?
 Inscribed Angle Theorem [01/21/1999]

Can you help me prove that an angle inscribed on the same arc as a
central angle is equal to one half that central angle?
 Inscribing a Regular Pentagon within a Circle [04/15/1999]

What are the reasons for the steps in inscribing a regular pentagon
within a circle with only the help of a compass and a straightedge?
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