Question 13
Two circles $\omega_1$ and $\omega_2$ intersect at points $A$ and $B$. A line through $B$ intersects $\omega_1$ at the point $C$ and $\omega_2$ at the point $D$. The line $AD$ intersects $\omega_1$ at a point $E$ different from $A$ and the line $AC$ intersects $\omega_2$ at a point $F$ different from $A$. If $O$ is the circumcenter of triangle $AEF$, prove that $OB \perp CD$.
(Proposed by B. Bat-Od)
(Proposed by B. Bat-Od)