Question 150
The two circles $\omega_1$ and $\omega_2$ touch each other externally at point $O$. Let $A$ and $B$ be points on $\omega_1$, and $C$ and $D$ be points on $\omega_2$ such that lines $AC$ and $BD$ are common external tangents to the circles. Line $AO$ intersects segment $CD$ at point $M$, while line $CO$ intersects $\omega_1$ at points $O$ and $N$. Prove that points $B$, $M$, and $N$ are collinear.