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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?



Area under Arc of Circle [02/27/2001]
Calculate the area delimited by the arc of a circle and the chord of that arc, given only the length of the chord and the length of a line, perpendicular to the chord, running from the middle of the chord to the edge of the circle.

Bounding Rectangle for an Ellipse [6/28/1996]
I would like to know if there is a general equation for a bounding rectangle of an ellipse.

Building a Circular Horse Pen [06/16/2002]
My Dad and I are building a round pen for our horse. We have 16 16ft. panels and a 10 ft. gate and a 4ft. gate. (270 ft. total) We want to use a radius and mark the places to dig holes for each post that will support the panels, but we don't know how long the radius should be. Can you help?

Building a Cone [10/28/2001]
I am trying to find a formula for building a cone for a chimney flashing. It should be 21" tall with a top opening of 8", a bottom opening of 20", and a vertical seam overlap of 2".

Calculating Circle Radius [01/29/2001]
I am trying to find a formula that will give me the radius of a circle, given only the length of an arc on that circle and the chord length of that arc.

Calculating the Radius from a Chord [08/18/1998]
If I know the chord length and chord height, is there a formula for determining the radius of the circle?

Can a Circle be a Polygon? [5/22/1996]
Could a circle be considered a polygon with an infinite number of sides?

Catenary and Parabola Comparison [04/06/2004]
What is the difference between a catenary and a parabola? I don't know the difference in shape. Why is the St. Louis arch a catenary and not a parabola?

Centering Circles [10/05/2002]
Two metal disks need to be centered on each other, but the circle with the larger diameter has the center cut out. How can you center them by knowing the diameters?

Center of a Circle from Circumference Points [06/25/1999]
How do I figure the center point (Xc,Yc,Zc) of a circle given 2 or more points on its circumference and its radius?

Center of Mass of a Semicircle [06/14/1999]
Is there a standard formula I can use to know where the center of mass of a semicircle is?

Changing Angle of a Tank [06/11/2003]
Points A and B represent pressure sensors in fixed positions on the base of a round tank. The chord through CD represents the water level in the tank. Lines a and b are the heights of water registered by each sensor...

Chord Proofs [10/07/1997]
Prove that in any circle a radius perpendicular to a chord also bisects the chord... a radius that bisects the chord is perpendicular to the chord... chords equidistant from the center of the circle are congruent.

Chords From Inscribed Polygons [07/11/2002]
An regular polygon is inscribed in a circle of known radius. Each side of the octagon is a chord of the circle. What is the length of each chord?

Circle and Polygons: Lines of Symmetry [04/14/1997]
How many lines of symmetry are there in a circle?

Circle Center's Cartesian Coordinates [03/24/1999]
How do you find the Cartesian coordinates of a circle's centers if you know two points on its perimeter?

Circle Enclosed by Three Circles [08/18/1999]
How can I find the center and radius of a circle that is enclosed by three other circles that all touch each other at one point?

Circle Geometry [6/4/1996]
Two circles intersect at A and N. One of their common tangents has points of contact P and T. Prove that <PAT and <PNT are supplementary.

Circle in n Sectors [7/8/1996]
A circle is completely divided into n sectors in such a way that the angles of the sectors are in arithmetic progression...

Circle Inscribed in a Right Triangle [09/09/1997]
What is the diameter of the circle if the legs of the triangle are known to be A and B?

Circle Inscribed in Sector [05/20/1999]
Given a 60-degree arc of a sector of a circle with a radius of 12 inches, find the area of the circle that can be inscribed in the sector.

Circle Inscribed in Triangle [04/04/1997]
What is the radius of a circle inscribed in a 3-4-5 right triangle?

Circle Overlap [11/08/2001]
Circle A and Circle B both have a radius of 1 unit. The centers of each circle are 1 unit apart as well. Find the area of the union of the two circles.

Circle Radius from Chord Length and Depth [06/16/1999]
How do you find the radius or diameter of a circle when you only know a chord length and the depth?

Circle Regions [01/28/2001]
What is the maximum number of regions you can have with n chords in a circle?

Circle Revolutions [07/02/2002]
Our teacher gave everyone a CD, and told us to look at the spin of the smaller inner circle and of the large outer circle. We have concluded that they both make a revolution in the same amount of time, but they moving at different speeds. Is that possible?

Circles around a Larger Circle [07/26/2003]
Is there a formula to determine the diameter of several smaller circles outlining the circumference of a larger circle?

Circle Sector Area [03/20/2003]
Do we have to convert degrees to radians when finding the area of a sector of a circle?

Circles in a Square [09/15/2001]
A circle of radius 1 is inside a square whose side has length 2. Show that the area of the largest circle that can be inscribed between the circle and the square is (pi(17 - 12sqrt(2))).

Circles Inscribed in Triangles [11/14/1996]
Given two triangles, prove that r1 + r2 + r3 = r.

Circles of More than 360 Degrees [11/10/2001]
What shape is formed if one cuts along the radius of a circle and adds degrees by adding a sector?

Circles within a Circle [10/12/2000]
Given three circles of diameters 3", 2", and 1", the two smaller inside the largest so that their combined diameters equal the diameter of the largest circle. What is the greatest possible diameter of a fourth circle placed in the remaining area?

Circle Tangent to Line [04/19/2001]
Construct the circle that passes through two given points and is tangent to a line.

Circle With Radius of Zero [12/28/2004]
Is it possible for a circle to have a radius that equals zero? Is it possible for a set of points to occupy the same location?

Circular Field, Cow, and Length of Rope [9/11/1996]
A cow is tied with a rope to the edge of a circular field 10 ft. in diameter. How long must the rope be so the cow can graze half the field?

Circumference and Rotation [10/07/2003]
The wheel on a truck rotates 330 times in a mile. Find the radius of the tire.

Circumference of a Circle Given Chord Length [9/11/1996]
Given the length of a chord of a circle, is it possible to determine the circumference?

Circumference of an Ellipse [5/18/1996]
Is there a formula for determining the circumference or distance around an ellipse?

Circumference of a Square [05/13/2002]
A circle has a circumference C. Find, in terms of C, the perimeter of a square having the same area as the circle.

Circumscribing Tangent Circles [04/13/1999]
Given three circles of various sizes in a plane, circumscribe a circle about them.

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