MathNet 2022-part-02 — 197 problems (EN–VI) Question 113

Let $ABC$ be a triangle whose angles are acute, and let $D$ be a point inside triangle $ABC$. The lines $(AD)$ and $(BD)$ meet the circumcircle of triangle $ABC$ again at the points $A_{1}$ and $B_{1}$ respectively. The circumcircle of triangle $B_{1}DA$ meets the line $(AC)$ again at the point $P$. The circumcircle of triangle $A_{1}BD$ meets the line $(BC)$ again at the point $Q$.

Prove that the quadrilateral $CPDQ$ is a parallelogram.