Question 31
Two circles $k_1,k_2$, with centers $M_1,M_2$ respectively, intersect at $A,B$. The tangent to $k_1$ at $A$ meets $k_2$ again at $P$. The line $M_1B$ meets $k_2$ again at $Q$. Suppose $Q$ is outside $k_1$ and $P\ne Q$. Prove that $PQ\parallel M_1M_2$.