__Category__: Plane Geometry"Published in Newark, California, USA"

A circle can be drawn through points X, Y, and Z.

a. What is the radius of the circle?

b. How far is the center of the circle from point W?

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__Solution__:

Consider the given figure above

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Expand the line segment YW from point W and label the other point as point V.

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If a theorem says "When two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other chord.", then the working equation is

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From the figure, by using Pythagorean Theorem, the distance of C from W is

and the radius of a circle which is the distance of C from Z is

If you will get the distance of C from X, Y, or V, the value of length must be the same otherwise point C is not the center of a circle.

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