MathDB
Inequality of Areas of triangle formed by circumcentres

Source:

December 9, 2010
inequalitiesgeometryinequalities unsolved

Problem Statement

Let MM be an interior point of a △ABC\triangle ABC such that ∠AMB=150∘,∠BMC=120∘\angle AM B = 150^{\circ} , \angle BM C = 120^{\circ}. Let P,Q,RP, Q, R be the circumcentres of the △AMB,△BMC,△CMA\triangle AM B, \triangle BM C, \triangle CM A respectively. Prove that [PQR]≥[ABC][P QR] \ge [ABC].
Back to ProblemsView on AoPS