document.write( "Question 763342: three circles are tangent externally.the distances between their centers are 23 inches,25 inches,20 inches.find their radii. \n" ); document.write( "

Algebra.Com's Answer #464705 by ramkikk66(644) $\"\"$ $\"About$

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If the 3 circles are externally tangential to each other, then it means that the line connecting their centers passes through the tangential point.\r
\n" ); document.write( "\n" ); document.write( "Which means that the distance between their centers is anyway equal to the sum of their radii.\r
\n" ); document.write( "\n" ); document.write( "So, if x, y, z are the radii of the 3 circles,\r
\n" ); document.write( "\n" ); document.write( "x + y = 23 ---- eqn(1)
\n" ); document.write( "y + z = 25 ---- eqn(2)
\n" ); document.write( "x + z = 20 ---- eqn(3)\r
\n" ); document.write( "\n" ); document.write( "Adding the above 3 equations, we get 2*x + 2*y + 2*z = 68, or x + y + z = 34 ---(eqn 4)\r
\n" ); document.write( "\n" ); document.write( "From (1) and (4), we get 23 + z = 34 or z = 11
\n" ); document.write( "From (2) and (4), we get 25 + x = 34 or x = 9
\n" ); document.write( "From (3) and (4), we get 20 + y = 34 or y = 14\r
\n" ); document.write( "\n" ); document.write( "So the radii of the 3 circles are $\"highlight%2811%29\"$ $\"highlight%289%29\"$ $\"highlight%2814%29\"$ \r
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