document.write( "Question 1066898: 2 Circular with centres A and B are touching externally.A circle with centre C touches both the circle externally. Suppose AB=3cm,BC=3cm and AC=4cm. Find the radii of the circles. \n" ); document.write( "

Algebra.Com's Answer #682128 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "2 $\"highlight%28cross%28Circular%29%29\"$ circles with $\"highlight%28cross%28centres%29%29\"$ centers A and B are touching externally.
\n" ); document.write( "A $\"highlight%28third%29\"$ circle with $\"highlight%28cross%28centre%29%29\"$ center C touches both the $\"highlight%28cross%28circle%29%29\"$ circles externally.
\n" ); document.write( "Suppose AB=3cm, BC=3cm and AC=4cm.
\n" ); document.write( "Find the radii of the circles.
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document.write( "When two circles touch externally, the distance between their center is the sum of their radii.\r\n" );
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document.write( "It gives you the system of three equations\r\n" );
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document.write( "a + b = 3,     (1)\r\n" );
document.write( "a + c = 4,     (2)\r\n" );
document.write( "b + c = 3.     (3)\r\n" );
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document.write( "where a, b and c are the radii of the three circles with the centers A, B and C respectively.\r\n" );
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document.write( "To solve the system, first add all the three equations. You will get\r\n" );
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document.write( "2a + 2b + 2c = 3 + 4 + 3 = 10,\r\n" );
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document.write( "which implies \r\n" );
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document.write( "a + b + c = 5.   (4)\r\n" );
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document.write( "Now extract equation (3) from equation (4) (both sides). You will get a = 5-3 = 2.\r\n" );
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document.write( "    Extract equation (2) from equation (4) (both sides). You will get b = 5-4 = 1.\r\n" );
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document.write( "Finally, extract equation (1) from equation (4) (both sides). You will get a = 5-3 = 2.\r\n" );
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document.write( "Answer.  The radii are: 2 cm for the circle with the center at A;\r\n" );
document.write( "         1 cm for the circle with the center at B;\r\n" );
document.write( "         2 cm for the circle with the center at C\r\n" );
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