IMO 2007 Problem 4
IMO 2007 Problem 4 is a plane geometry problem from the International Mathematical Olympiad 2007, Problem 4: equal areas from the bisector of angle C.
Problem
In triangle $ABC$ the bisector of angle $BCA$ intersects the circumcircle again at $R$, the perpendicular bisector of $BC$ at $P$, and the perpendicular bisector of $AC$ at $Q$. The midpoint of $BC$ is $K$ and the midpoint of $AC$ is $L$. Prove that the triangles $RPK$ and $RQL$ have the same area.
Source International Mathematical Olympiad 2007, Problem 4
The diagram
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