Question 80
In an acute $\triangle ABC$ with $CA \neq CB$ and incenter $O$ denote by $A_1$ and $B_1$ the tangent points of its excircles to the sides $CB$ and $CA$, respectively. The line $CO$ meets the circumcircle of $\triangle ABC$ at point $P$ and the line through $P$ which is perpendicular to $CP$ meets the line $AB$ at point $Q$. Prove that the lines $QO$ and $A_1B_1$ are parallel.