document.write( "Question 194449: Two circles intersect and have a common chord. THe radii of the circles are 13 cm and 15 cm. The distance between their centers is 14 cm. Find the length of their common chord. I already drew the picture. I drew two circles intersecting each other like a venn diagram. Then, i connected the two centers and that equals 14 and drew a line from the center of each circle to an edge of the circle equaling the radius of each circle. Then, I drew a dashed line down the intersection of the two circles in the middle and a perpendicular line shows up with the line connected by the center. What step am I supposed to take from there? \n" ); document.write( "

Algebra.Com's Answer #145909 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Let the circles' centers be A and B.\r\n" );
document.write( "Draw the common chord CD. Draw radii AC and BC.\r\n" );
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document.write( "We know that , ,  \r\n" );
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document.write( "We are given all three sides of triangle ABC, so\r\n" );
document.write( "we can use the law of cosines to find cos(A)\r\n" );
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document.write( "We know that the line through their centers\r\n" );
document.write( "is the perpendicular bisector of the common \r\n" );
document.write( "chord CD.  \r\n" );
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document.write( "This tells us two things. \r\n" );
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document.write( "1. If we find CE we can just\r\n" );
document.write( "double it to get the common chord CD.  \r\n" );
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document.write( "2. Triangle AEC is a right triangle and therefore\r\n" );
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document.write( "Now we use the identity \r\n" );
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document.write( "Substitute  for \r\n" );
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document.write( "Now we substitute that in\r\n" );
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document.write( "CE is half the common chord CD, so\r\n" );
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document.write( "the common chord CD is twice CE or \r\n" );
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document.write( "2x12 or 24.\r\n" );
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document.write( "Edwin

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