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The radius $r$ of a circle inscribed within three mutually externally tangent circles of radii $a$, $b$ and $c$ is given by
\[r = \sqrt{ab + ac + bc}.\]
What is the value of $r$ when $a = 4$, $b = 9$ and $c = 36$?

 Aug 9, 2023
 #1
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r =sqrt  (ab+ac + bc)  =  sqrt ( 4*9 + 4*36 + 9*36)  = sqrt (36 + 4*36 + 9 *36) = sqrt [ 36 (1+ 4 + 9) ] =

 

6 sqrt [ 14 ]

 

 

cool cool cool

 Aug 9, 2023

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