document.write( "Question 1149754: The figure ABCD is a rectangle, AD = 6, AB = 18, arc AB is a semicircle with
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Algebra.Com's Answer #771177 by Edwin McCravy(20064)\"\" \"About 
You can put this solution on YOUR website!
The drawing below is to scale.  The one given is not.\r\n" );
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document.write( "Let O be the center of the larger semicircle.\r\n" );
document.write( "Let P be the center of the smaller semicircle.\r\n" );
document.write( "Draw OP which will pass through the common point of tangency T and will\r\n" );
document.write( "be perpendicular to tangent EG.\r\n" );
document.write( "Let the radius of the small semicircle be r = CP = TP = FP\r\n" );
document.write( "Since AB = 18, the diameter of the larger semicircle, the radius = OB = 9.\r\n" );
document.write( "OB² + BP² = OP²\r\n" );
document.write( "9² + (BC-CP)² = (OT+TP)²\r\n" );
document.write( "9² + (6-r)² = (9+r)²\r\n" );
document.write( "Solve that and get r = CP = TP = FP = 1.2\r\n" );
document.write( "Triangles OBP and GTP are similar right triangles for they have\r\n" );
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document.write( "\"%28PG%29%2F%28PO%29+=+%28TP%29%2F%28PB%29\"\r\n" );
document.write( "\"%28PG%29%2F%28OT%2BTP%29=%281.2%29%2F%28BC-CP%29\"\r\n" );
document.write( "\"%28PG%29%2F%289%2B1.2%29=1.2%2F%286-1.2%29\"\r\n" );
document.write( "Solve that and get PG=2.55\r\n" );
document.write( "CG = CP + PG\r\n" );
document.write( "CG = 1.2+2.55\r\n" );
document.write( "CG = 3.75\r\n" );
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document.write( "Triangles GTP and GCE are similar right triangles for they have\r\n" );
document.write( "a common acute angle at G.  And since right triangles OBP and GTP \r\n" );
document.write( "are similar, GCE and OBP are similar, so\r\n" );
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document.write( "\"%28EC%29%2F%28CG%29+=+%28BP%29%2F%28OB%29\"\r\n" );
document.write( "\"%28EC%29%2F%28PG%2BCP%29=%28BC-CP%29%2F%28OB%29\"\r\n" );
document.write( "\"%28EC%29%2F%282.55%2B1.2%29=%286-1.2%29%2F9\"\r\n" );
document.write( "Solve that and get EC=2\r\n" );
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document.write( "Edwin
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