document.write( "Question 1153286: Three circles are mutually tangent to one another externally. Their centers are connected forming a triangle whose sides are 16 cm, 20 cm, and 24 cm. Find the area of the largest circle.\r
\n" ); document.write( "\n" ); document.write( "A. 804.25 cm2
\n" ); document.write( "B. 615.75 cm2
\n" ); document.write( "C. 452.25 cm2
\n" ); document.write( "D. 314.16 cm2 \n" ); document.write( "

Algebra.Com's Answer #775484 by ikleyn(52787) $\"\"$ $\"About$

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Three circles are mutually tangent to one another externally. Their centers are connected forming a triangle
\n" ); document.write( "whose sides are 16 cm, 20 cm, and 24 cm. Find the area of the largest circle.\r
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\n" ); document.write( "\n" ); document.write( "A. 804.25 cm2
\n" ); document.write( "B. 615.75 cm2
\n" ); document.write( "C. 452.25 cm2
\n" ); document.write( "D. 314.16 cm2
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document.write( "Let \"a\", \"b\" and \"c\" be the radii of these circles.\r\n" );
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document.write( "Notice that each segment connecting the centers of any two of the three given circles has the length equal to the sum of the related radii.\r\n" );
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document.write( "Therefore, we have these three equations for 3 unknowns \"a\", \"b\" and \"c\"\r\n" );
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document.write( "    a + b = 16,     (1)\r\n" );
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document.write( "    a + c = 20,     (2)\r\n" );
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document.write( "    b + c = 24.     (3)\r\n" );
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document.write( "To solve the system, add all three equations (1), (2) and (3).\r\n" );
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document.write( "You will get \r\n" );
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document.write( "    2a + 2b + 2c = 16 + 20 + 24,\r\n" );
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document.write( "    2*(a + b + c) = 60.\r\n" );
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document.write( "hence,\r\n" );
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document.write( "    a + b + c = 30.    (4)\r\n" );
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document.write( "To find \"a\", subtract equation (3) from equation (4). You will get  a = 30-24 = 6.\r\n" );
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document.write( "Then from (1),  b = 16-6 = 10  and from (2)  c = 20-6 = 14.\r\n" );
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document.write( "The area of the largest circle is   =  = 615.75 cm^2    (approximately).    ANSWER\r\n" );
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