Question 64
Let $O_1$ be the centre of the circle $K_1$. Let $K_2$ be the circle centered at $O_2$ and passing through $O_1$. The circles $K_1$ and $K_2$ meet at $A$ and $B$. The circle $K_1$ intersects the segment $O_1O_2$ at $C$. The line $BC$ intersects the circle $K_2$ at $B$ and $D$. The line $AD$ intersects the circle $K_1$ at $A$ and $E$. Let $F$ be the midpoint of the segment $AE$. Prove that the lines $O_1A$ and $O_1D$ divide the angle $CO_1F$ into three equal parts.