Problem

Source: Sharygin 2019 Finals Day 1 Grade 9 P1

Tags: geometry, Sharygin Geometry Olympiad



A triangle $OAB$ with $\angle A=90^{\circ}$ lies inside another triangle with vertex $O$. The altitude of $OAB$ from $A$ until it meets the side of angle $O$ at $M$. The distances from $M$ and $B$ to the second side of angle $O$ are $2$ and $1$ respectively. Find the length of $OA$.