[ Thales' Theorem and the Proportional Segments Theorem ] The Midline of a Triangle

In triangle $A B C$, point $M$ is the midpoint of side $A C$, and 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 $O M: P C$.
## Answer

$1: 2$.