document.write( "Question 166477: The radius of a circle is 5 and its center is at (-3,-4). Find the lenght of the chord that is bisected at (-11/12, -13/12). \n" ); document.write( "
Algebra.Com's Answer #122725 by nerdybill(7384)\"\" \"About 
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First, find the distance between the center and the bisected point is:
\n" ); document.write( "Do this using the \"distance formula\" between two points:
\n" ); document.write( "d = sqrt[(x2-x1)^2 + (y2-y1)^2]
\n" ); document.write( "(-3,-4) and (-11/12, -13/12)
\n" ); document.write( "d = sqrt[(-11/12+3)^2 + (-13/12+4)^2]
\n" ); document.write( "d = sqrt[(-11/12+36/12)^2 + (-13/12+48/12)^2]
\n" ); document.write( "d = sqrt[(25/12)^2 + (35/12)^2]
\n" ); document.write( "d = sqrt[4.34 + 8.51]
\n" ); document.write( "d = sqrt[12.85]
\n" ); document.write( "d = 3.584
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\n" ); document.write( "Drawing a diagram of the problem will help you see that the \"distance between the center and bisector\", \"half the chord\" and the \"radius\" forms a right triangle -- allowing you to apply the pythagorean theorem:
\n" ); document.write( "Let x = half the length of the chord
\n" ); document.write( "then
\n" ); document.write( "x^2 + 3.584^2 = 5^2
\n" ); document.write( "x^2 + 12.847 = 25
\n" ); document.write( "x^2 = 12.153
\n" ); document.write( "x = 3.486
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\n" ); document.write( "Length of chord is
\n" ); document.write( "2x = 2(3.486) = 6.972\r
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