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Question: The length of the chord AB = 12 in. Find the radius of the circle O.

A ) 62 in.
B ) 6 in.
C ) 7 in.
D ) 72 in.

Steps to derive

1 Length of chord AB = 12 in..

2 AOB is a right triangle.

 [Apply Pythagorean theorem.]
3 AB² = OA² + OB²

 [Since, the radius of the circle = OA = OB.]
4 AB² = 2OA²

5 OA² = AB22
 [Divide by 2 on both sides.]

6 OA² = 1222
 [Substitute AB.]

 [Apply exponents and simplify.]
7 OA² = 1442 = 72

8 OA = 72 = 62
 [Find the positive square root.]

9 The radius of the circle, O is 62 in.



Hence the right answer is Option A

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