Question 97
Let $ABCD$ be a parallelogram with $AC = BC$. Take a point $P$ on line $AB$ such that $B$ lies between $A$ and $P$. The circumcircle of triangle $ACD$ meets segment $PD$ again at $Q$, and the circumcircle of triangle $APQ$ meets segment $PC$ again at $R$.
Prove that the three lines $CD$, $AQ$, $BR$ are concurrent.
Prove that the three lines $CD$, $AQ$, $BR$ are concurrent.