Question 19
Let $(O_{1})$, $(O_{2})$ be given two circles intersecting at $A$ and $B$. The tangent lines of $(O_{1})$ at $A$, $B$ intersect at $O$. Let $I$ be a point on the circle $(O_{1})$ but outside the circle $(O_{2})$. The lines $IA$, $IB$ intersect circle $(O_{2})$ at $C$, $D$. Denote by $M$ the midpoint of $CD$. Prove that $I$, $M$, $O$ are collinear.