Question 85
Let $\omega_1$ and $\omega_2$ be two circles with centers $O_1$ and $O_2$, respectively, with $O_2$ lying on $\omega_1$. Let $A$ be a common point of $\omega_1$ and $\omega_2$. A line through $A$ intersects $\omega_1$ in $B \neq A$ and $\omega_2$ in $C \neq A$ such that $A$ lies between $B$ and $C$. The ray $O_2O_1$ intersects $\omega_2$ in $D$ and contains a point $E$ such that $\angle EAD = \angle DCO_2$ and $D$ lies between $O_2$ and $E$. Show that $BO_2$ bisects $CE$.