Question 55
Let $A$ be one of the intersection points of circles $\omega_1(O_1)$ and $\omega_2(O_2)$. $\ell$ is a line that touches $\omega_1$ and $\omega_2$ at $B$ and $C$ respectively. Let $O_3$ be the center of the circumscribed circle of $ABC$. And we choose $D$ as $A$ is midpoint of $O_3D$. If $M$ is midpoint of $O_1O_2$, then prove that $\angle O_1DM = \angle O_2DA$.