OSN 2005 Problem 4

Let $M$ be a point in triangle $ABC$ such that $\angle AMC=90^{\circ}$ , $\angle AMB=150^{\circ}$ , $\angle BMC=120^{\circ}$ . The centers of circumcircles of triangles $AMC,AMB,BMC$ are $P,Q,R$ , respectively. Prove that the area of $\triangle PQR$ is greater than the area of $\triangle ABC$ .