document.write( "Question 1137177: Inside a circle, with centre O and radius r, two circles with centres A and B are drawn, which touch each other externally and the given circle internally. Prove that the perimeter of the triangle AOB is 2r. \n" ); document.write( "

Algebra.Com's Answer #755036 by ikleyn(52800) $\"\"$ $\"About$

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document.write( "1.  Make a sketch.\r\n" );
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document.write( "2.  Let C be the point where the two small circles touch each other.\r\n" );
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document.write( "    Let  |AC| = x  (the unknown length - same as the radius of each of the two small circles).\r\n" );
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document.write( "    Then |BC| = x,  too.\r\n" );
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document.write( "    |AO| = r-x  and  |BO| = r-x    (OBVIOUS.  Use the sketch)\r\n" );
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document.write( "    The perimeter of the triangle AOB is equal to\r\n" );
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document.write( "        |AO| + |BO| + |AC| + | BC| = (r-x) + (r-x) + x + x = 2r.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Proved, explained, solved and completed.\r
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