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triangle geometry

Source: Poland Olympiad 1998

January 11, 2016
geometrygeometry proposed

Problem Statement

In triangle ABCABC, the angle ∠BCA\angle BCA is obtuse and ∠BAC=2∠ABC .\angle BAC = 2\angle ABC\,. The line through BB and perpendicular to BCBC intersects line ACAC in DD. Let MM be the midpoint of ABAB. Prove that ∠AMC=∠BMD\angle AMC=\angle BMD.
source : http://cage.ugent.be/~hvernaev/Olympiade/PMO982.pdf
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