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 $c = 36$?
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 ]
+817 
