document.write( "Question 1078647: As shown in the diagram, a circle with centre A and radius 9 is tangent to a smaller circle with centre D and radius 4. Common tangents EF and BC are drawn to the circles making points of contact at E, B and C. Determine the length of EF.\r
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Algebra.Com's Answer #693154 by Edwin McCravy(20060)\"\" \"About 
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document.write( "Now we draw in line DG (in green) parallel and equal to BC.\r\n" );
document.write( "It intersects EF at I.  DG divides radius AB = 9 into AG and BG. \r\n" );
document.write( "Since CD = BG = 4, AG = AB-BG = 9-4 = 5 \r\n" );
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document.write( "Now we use the Pythagorean theorem on right triangle AGD:\r\n" );
document.write( "Hypotenuse = AD = radius AE + radius DE = 9+4 = 13\r\n" );
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document.write( "DG2 + AG2 = AD2\r\n" );
document.write( "DG2 + 52 = 132\r\n" );
document.write( "DG2 + 25 = 169\r\n" );
document.write( "DG2 = 144\r\n" );
document.write( "DG = 12\r\n" );
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document.write( "Now we have BC = DG = 12.\r\n" );
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document.write( "Next, we draw in EH parallel to AB and CD and perpendicular\r\n" );
document.write( "to BC and G.  DG and EH are perpendicular and intersect at J \r\n" );
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document.write( "By similar triangles EJD and AGD,\r\n" );
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document.write( "\"EJ%2F%28AG%29=%22DE%22%2F%22AD%22\"\r\n" );
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document.write( "\"%22EJ%22%2F5=4%2F13\"\r\n" );
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document.write( "\"13%2A%22EJ%22=20\"\r\n" );
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document.write( "\"EJ=20%2F13\"\r\n" );
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document.write( "HJ = CD = 4\r\n" );
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document.write( "Therefore EH = EJ+HJ = \"20%2F13%2B4=20%2F13%2B52%2F13=72%2F13\"\r\n" );
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document.write( "Triangles IJE and EJD are similar since they are right\r\n" );
document.write( "triangles with a common angle at D.\r\n" );
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document.write( "Triangles IJE and FHE are similar\r\n" );
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document.write( "Therefore triangles FHE and AGD are similar\r\n" );
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document.write( "\"%22EF%22%2F%22EH%22=%22AD%22%2F%22DG%22\"\r\n" );
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document.write( "\"%22EF%22%2F%2872%2F13%29=13%2F12\"\r\n" );
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document.write( "\"EF%2Aexpr%2813%2F72%29=13%2F12\"\r\n" );
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document.write( "Divide both sides by 13\r\n" );
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document.write( "\"EF%2F72=1%2F12\"\r\n" );
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document.write( "\"EF=72%2F12\"\r\n" );
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document.write( "\"EF=6\"\r\n" );
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document.write( "Edwin
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