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Perpendiculars and Angle Bisectors

Source: Olimpiada de Mayo

June 4, 2012
geometryratioprojective geometryperpendicular bisectorgeometry unsolved

Problem Statement

Given Triangle ABCABC, ∠B=2∠C\angle B= 2 \angle C, and ∠A>90∘\angle A>90^\circ. Let MM be midpoint of BCBC. Perpendicular of ACAC at CC intersects ABAB at DD. Show ∠AMB=∠DMC\angle AMB = \angle DMC
If possible, don't use projective geometry
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