document.write( "Question 1207163: two circles intersect (a nd b) and share a common chord (cd). the radius of circle a is 10in, radius circle b = 16 in. distance between centers, 22 in. find cd. \n" ); document.write( "

Algebra.Com's Answer #844877 by ikleyn(52946) $\"\"$ $\"About$

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\n" ); document.write( "two circles intersect (A nd B) and share a common chord (CD).
\n" ); document.write( "the radius of circle a is 10in, radius circle b = 16 in. distance between centers, 22 in.
\n" ); document.write( "find cd.
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document.write( "Draw the radii of the circles from their centers to the intersection point C.\r\n" );
document.write( "Connect the centers by the straight line AB.\r\n" );
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document.write( "You will get a triangle ABC with the sides 10 in, 16 in and 22 in.\r\n" );
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document.write( "Find its area using the Heron's formula\r\n" );
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document.write( "    area = ,\r\n" );
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document.write( "where s =  = 24 is the semi-perimeter.\r\n" );
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document.write( "Substituting this number into the formula, you will get\r\n" );
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document.write( "    area =  =  =  = \r\n" );
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document.write( "         =  =  = 73.32121112... square inches.\r\n" );
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document.write( "Write the formula for the area of triangle ABC in other way, using the base AB = 22 in and the height h\r\n" );
document.write( "from point C to the base\r\n" );
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document.write( "    area =  = 11*h  square inches.\r\n" );
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document.write( "You will get an equation\r\n" );
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document.write( "    11*h = .\r\n" );
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document.write( "Hence,  \r\n" );
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document.write( "    h = .\r\n" );
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document.write( "This value of h is half of the length CD;  so\r\n" );
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document.write( "    CD =  = 13.331 inches  (rounded).\r\n" );
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document.write( "At this point, the problem is just solved.\r\n" );
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document.write( "ANSWER.  The length CD is   = 13.331 inches  (rounded).\r\n" );
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