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Congruent angles at a midpoint of a side in obtuse triangle

Source: Spanish Mathematical Olympiad, National Stage, 2011

August 9, 2011
ratiogeometrytrapezoidtrigonometryperpendicular bisectorangle bisectorgeometry unsolved

Problem Statement

In triangle ABCABC, ∠B=2∠C\angle B=2\angle C and ∠A>90∘\angle A>90^\circ. Let DD be the point on the line ABAB such that CDCD is perpendicular to ACAC, and let MM be the midpoint of BCBC. Prove that ∠AMB=∠DMC\angle AMB=\angle DMC.
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