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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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Photo by Math Principles in Everyday Life |
Expand the line segment YW from point W and label the other point as point V.
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Photo by Math Principles in Everyday Life |
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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Photo by Math Principles in Everyday Life |
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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Photo by Math Principles in Everyday Life |