BG-MO 1993 Problem 2

Let $M$ be an interior point of the triangle $ABC$ such that $AMC = 90^\circ$ , $AMB = 150^\circ$ , and $BMC = 120^\circ$ . The circumcenters of the triangles $AMC$ , $AMB$ , and $BMC$ are $P$ , $Q$ , and $R$ respectively. Prove that the area of $\Delta PQR$ is greater than or equal to the area of $\Delta ABC$ .