3. A circle $\omega$ with center at point $O$ is circumscribed around triangle $ABC$. Circle $\omega_{1}$ touches the line $AB$ at point $A$ and passes through point $C$, while circle $\omega_{2}$ touches the line $AC$ at point $A$ and passes through point $B$. A line through point $A$ intersects circle $\omega_{1}$ again at point $X$ and circle $\omega_{2}$ again at point $Y$. Point $M$ is the midpoint of segment $XY$. Find the angle $OMX$.