Mongolian National Mathematical Olympiad

Two circles ${\omega }_1$ and ${\omega }_2$ intersected at points $A$ and $B$. Line through $B$ is intersect the ${\omega }_1$ at point $C$ and intersect the ${\omega }_2$ at point $D$. The line $AD$ intersect the ${\omega }_1$ at point $E$ different from $A$ and the line $AC$ intersect the ${\omega }_2$ at point $F$ different from $A$. If $O$ is circumcenter of triangle $AEF$ then prove that $OB\perp CD$.

(Proposed by B. Bat-Od)