Question 106
Let $ABCD$ be a parallelogram such that $AC = BC$. Let $P$ be a point on the extension of the segment $[AB]$ beyond $B$. Let $Q$ be the intersection point, other than $D$, of the segment $[PD]$ and the circumcircle of $ACD$. Then let $R$ be the intersection point, other than $P$, of the segment $[PC]$ and the circumcircle of $APQ$.
Prove that the lines $(AQ)$, $(BR)$ and $(CD)$ are concurrent.
Prove that the lines $(AQ)$, $(BR)$ and $(CD)$ are concurrent.