Question 16
Let $K_1$ have centre $O_1$, and let circle $K_2$ with centre $O_2$ pass through $O_1$. They meet at $A,B$. Circle $K_1$ meets segment $O_1O_2$ at $C$. Line $BC$ meets $K_2$ again at $D$; line $AD$ meets $K_1$ again at $E$. Let $F$ be the midpoint of $AE$. Prove that lines $O_1A,O_1D$ trisect $\angle CO_1F$.