In triangle $A B C A B=15, B C=12, A C=18$. In what ratio does the center $O$ of the inscribed circle of the triangle divide the bisector $C M$?
$A M: M B=A C: C B=3: 2$. Therefore $A M=3 / 5 A B=9, O C: O M=A C: A M=2: 1$ (since $A O$ is the bisector of triangle AMC).

## Answer

$2: 1$.