Ask Dr. Math

High School Archive

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?

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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 cross-section 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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