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Geometric Inequality on Angles - Iran NMO 2009 - Problem 3

Source:

September 20, 2010
inequalitiesgeometrycircumcircletrigonometryangle bisectorgeometry proposedGeometric Inequalities

Problem Statement

Let ABC ABC be a triangle and the point D D is on the segment BC BC such that AD AD is the interior bisector of ∠A \angle A . We stretch AD AD such that it meets the circumcircle of ΔABC \Delta ABC at M M . We draw a line from D D such that it meets the lines MB,MC MB,MC at P,Q P,Q , respectively (M M is not between B,P B,P and also is not between C,Q C,Q ). Prove that ∠PAQ≥∠BAC \angle PAQ\geq\angle BAC .
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