Volovich M.A.

In triangle $A B C$, point $M$ is the midpoint of side $A C$, point $P$ lies on side $B C$. Segment $A P$ intersects $B M$ at point $O$. It turns out that $B O=B P$.

Find the ratio $O M: P C$.
Let's draw the midline $M N$ of triangle $A C P$ (parallel to $A P$). By Thales' theorem, $O M: P N = B O: B P$, therefore $O M = P N = 1 / 2 P C$.

## Answer

$1: 2$.