SOLUTION: Suppose a chord of a circle is 24 inches long and is 9 inches from the center. Find the length of the radius.

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Question 87727: Suppose a chord of a circle is 24 inches long and is 9 inches from the center. Find the length of the radius.
Answer by tutor_paul(519)   (Show Source): You can put this solution on YOUR website!
The 9 inch distance from the center of the circle to the chord is called the "Apothem" The apothem bisects the chord and is perpendicular to it. So if you draw this out, you will see you have a right triangle formed by the apothem (9), half of the chord (12), and the radius (which is the hypotenuese). So, you can solve for the radius via the pythagorean theorem:


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You could also recognize that this is a 3-4-5 times 3 right triangle, and see that the hypotenuese is 15. This saves you time from working out the pythogorean theorem.
Good Luck,
tutor_paul@yahoo.com

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