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Double angles and lengths

Source: Sharygin Geometry Olympiad 2012 - Problem 1

April 28, 2012
geometrygeometric transformationhomothetycircumcircleangle bisectorgeometry unsolved

Problem Statement

In triangle ABCABC point MM is the midpoint of side ABAB, and point DD is the foot of altitude CDCD. Prove that ∠A=2∠B\angle A = 2\angle B if and only if AC=2MDAC = 2 MD.
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