SOLUTION: A circle has a chord of length 10 cm. This chord is the perpendicular bisector of a radius of that circle. What is the area of the circle in square centimeters?

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Question 355100: A circle has a chord of length 10 cm. This chord is the perpendicular bisector of a radius of that circle. What is the area of the circle in square centimeters?
Answer by robertb(5830) About Me  (Show Source):
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The given chord perpendicularly bisects a radius of the circle, so we can form a right triangle where one leg measures 5 cm, the other leg measures r%2F2, and the hypotenuse measures r. Then by the Pythagorean Theorem,
r%5E2+=+%28r%2F2%29%5E2+%2B5%5E2,
r%5E2+=+r%5E2%2F4%2B25,
3r%5E2%2F4+=+25,
r%5E2+=+100%2F3.
Now the area of the circle is given by A+=+pi%2Ar%5E2.
Substituting r%5E2+=+100%2F3 into this area formula, we get
A+=+100pi%2F3square centimeters.