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Point M in Triangle ABC

Source: Indonesia Mathematics Olympiad 2005 Day 1 Problem 4

June 2, 2008
geometrycircumcircletrigonometrygeometry proposed

Problem Statement

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