SOLUTION: In a cirlcle whose diameter is 20 inches, a chord is 6 inches from the center. What is the length of the chord?

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Question 551319: In a cirlcle whose diameter is 20 inches, a chord is 6 inches from the center. What is the length of the chord?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Connect the end points of the chord to the center of the circle then draw the angle bisector from the center perpendicular to the chord thus bisecting the chord.
You now have two congruent right triangles in which the hypotenuse is the radius of the circle (10 inches), and whose height is 6 inches.
Using the Pythagorean theorem: c%5E2+=+a%5E2%2Bb%5E2 where c = 10, a = 6, and b = half the length of the chord.
10%5E2+=+6%5E2%2Bb%5E2
b+=+sqrt%28100-36%29
b+=+sqrt%2864%29
b+=+8
The chord is 2(8) = 16 inches.