document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #359641 by Earlsdon(6294) $\"\"$ $\"About$

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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.
\n" ); document.write( "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.
\n" ); document.write( "Using the Pythagorean theorem: $\"c%5E2+=+a%5E2%2Bb%5E2\"$ where c = 10, a = 6, and b = half the length of the chord.
\n" ); document.write( " $\"10%5E2+=+6%5E2%2Bb%5E2\"$
\n" ); document.write( " $\"b+=+sqrt%28100-36%29\"$
\n" ); document.write( " $\"b+=+sqrt%2864%29\"$
\n" ); document.write( " $\"b+=+8\"$
\n" ); document.write( "The chord is 2(8) = 16 inches. \r
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