document.write( "Question 1111549: Three circles C1,C2,C3 are externally tangent to each other. Center-to-center distances are 10 cm between C1 and C2 , 8 cm between C2 and C3 , and 6 cm between C3 and C1. Determine the total areas of the circles. \n" ); document.write( "

Algebra.Com's Answer #726561 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "What you need is to find the radii of the circles.\r
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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 = 10,     (1)\r\n" );
document.write( "a + c =  8,     (2)\r\n" );
document.write( "b + c =  6.     (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 = 10 + 8 + 6 = 24,\r\n" );
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document.write( "which implies \r\n" );
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document.write( "a + b + c = 12.   (4)\r\n" );
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document.write( "Now subtract equation (3) from equation (4) (both sides). You will get c = 12-10 = 2.\r\n" );
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document.write( "    Subtract equation (2) from equation (4) (both sides). You will get b = 12-8 = 4.\r\n" );
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document.write( "Finally, subtract equation (1) from equation (4) (both sides). You will get a = 12-6 = 6.\r\n" );
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document.write( "Now the area under the question is   = 175.84 cm^2.\r\n" );
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\n" ); document.write( "To see similar solved problems, look into the lesson\r
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