Question 4
(BEL 5) On the sides of the triangle $ABC$, three similar isosceles triangles $ABP$ $(AP=PB)$, $AQC$ $(AQ=QC)$, and $BRC$ $(BR=RC)$ are constructed. The first two are constructed externally to the triangle $ABC$, but the third is placed in the same half-plane determined by the line $BC$ as the triangle $ABC$. Prove that $APRQ$ is a parallelogram.