document.write( "Question 765501: Two parallel chords on the same side of the centre of a circle are 5 cm apart. If the chords are 20 and 28 cm long, what is the radius of the circle? \n" ); document.write( "
Algebra.Com's Answer #466237 by Edwin McCravy(20056)\"\" \"About 
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document.write( "Draw the two chords. Let O be the center of the circle.  Draw OC \r\n" );
document.write( "perpendicular to both chords. That divides the two chords in half.\r\n" );
document.write( "So CD = 10 and AB = 14.  Draw radii OA and OD, both equal to radius r.\r\n" );
document.write( "We are given that BC = 5, the distance between the two chords.  Let\r\n" );
document.write( "OB = x.\r\n" );
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document.write( "We use the Pythagorean theorem on right triangle ABO\r\n" );
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document.write( "AO² = AB² + OB²\r\n" );
document.write( " r² = 14² + x²\r\n" );
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document.write( "We use the Pythagorean theorem on right triangle DCO\r\n" );
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document.write( "DO² = CD² + OC²\r\n" );
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document.write( "We see that OC = OB+BC = x+5, so\r\n" );
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document.write( " r² = 10² + (x+5)²\r\n" );
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document.write( "So we have a system of two equations:\r\n" );
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document.write( "  r² = 14² + x²\r\n" );
document.write( "  r² = 10² + (x+5)²\r\n" );
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document.write( "Since both left sides equal r², set the right sides\r\n" );
document.write( "equal to each other. \r\n" );
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document.write( " 14² + x² = 10² + (x+5)²\r\n" );
document.write( " 196 + x² = 100 + x² + 10x + 25\r\n" );
document.write( "      196 = 125 + 10x\r\n" );
document.write( "       71 = 10x\r\n" );
document.write( "      7.1 = x\r\n" );
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document.write( "       r² = 14² + x²\r\n" );
document.write( "       r² = 196 + (7.1)²\r\n" );
document.write( "       r² = 196 + 50.41\r\n" );
document.write( "       r² = 246.41\r\n" );
document.write( "        r = √246.41\r\n" );
document.write( "        r = 15.69745202 cm \r\n" );
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document.write( "Edwin
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