document.write( "Question 858267: Pleas help me to solve this question: AB and CD are two parallel chords of a circle. If AB = 24 cm, CD = 10 cm and distance between these chords is 17 cm, find the radius of the circle. \n" ); document.write( "
Algebra.Com's Answer #517166 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "She hasn't learned how to draw on here yet.\r\n" );
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document.write( "Draw EF through O perpendicular to AB and CD,\r\n" );
document.write( "also draw radii OA and OC.  EF is the perpendicular\r\n" );
document.write( "bisector of the chords, so that AE=12 and CF=5.\r\n" );
document.write( "Label the radii r and label OE and OF as x and y, \r\n" );
document.write( "respectively.\r\n" );
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document.write( "Using the Pythagorean theorem on the two right triangles OEA and OFC\r\n" );
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document.write( "x² + 12² = r²\r\n" );
document.write( " y² + 5² = r²\r\n" );
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document.write( "Simplify and subtract the two equations:\r\n" );
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document.write( "  x²  + 144 = r²\r\n" );
document.write( "  y²  +  25 = r²\r\n" );
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document.write( "x²-y² + 119 = 0\r\n" );
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document.write( "      x²-y² = -119\r\n" );
document.write( " Factor the left side:\r\n" );
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document.write( " (x-y)(x+y) = -119\r\n" );
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document.write( "We are given that EF = 17 = x+y, so\r\n" );
document.write( "we can substitute 17 for (x+y)\r\n" );
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document.write( "  (x-y)(17) = -119\r\n" );
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document.write( "Divide both sides by 17\r\n" );
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document.write( "        x-y = -7 , add that equation to\r\n" );
document.write( "        x+y = 17\r\n" );
document.write( "      -----------\r\n" );
document.write( "       2x   = 10\r\n" );
document.write( "          x = 5\r\n" );
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document.write( "Substitute in x+y = 17 and get y  = 12.\r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "      y²+25 = r²\r\n" );
document.write( "     12²+25 = r²\r\n" );
document.write( "     144+25 = r²\r\n" );
document.write( "        169 = r²\r\n" );
document.write( "         13 = r\r\n" );
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document.write( "Answer: the radius is 13 cm. \r\n" );
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document.write( "Edwin
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