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Geometric inequality proof

Source: Bulgaria 1993

April 23, 2006
inequalitiesgeometrycircumcircletrigonometry

Problem Statement

Let MM be an interior point of the triangle ABCABC such that AMC=90∘AMC = 90^\circ, AMB=150∘AMB = 150^\circ, and BMC=120∘BMC = 120^\circ. The circumcenters of the triangles AMCAMC, AMBAMB, and BMCBMC are PP, QQ, and RR respectively. Prove that the area of ΔPQR\Delta PQR is greater than or equal to the area of ΔABC\Delta ABC.
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