Question 4
In triangle $ABC$ the bisector of $\angle BCA$ meets the circumcircle again at $R$, the perpendicular bisector of $\overline{BC}$ at $P$, and the perpendicular bisector of $\overline{AC}$ at $Q$. The midpoint of $\overline{BC}$ is $K$ and the midpoint of $\overline{AC}$ is $L$. Prove that the triangles $RPK$ and $RQL$ have the same area.