Question 108
Let $ABCD$ be a parallelogram. A line $d$ through $C$ meets the lines $(AB)$ and $(AD)$ at $X$ and $Y$ respectively. The tangents at $X$ and at $Y$ to the circumcircle of $AXY$ meet at a point $T$, and then the line $(CT)$ meets the circumcircle of $CDY$ again at a point $P$.
Prove that the points $A, B, D$ and $P$ are concyclic.
Prove that the points $A, B, D$ and $P$ are concyclic.