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Reflection point is on the median

Source: 2015 Turkey Junior National Olympiad P4

December 7, 2015
geometrygeometric transformationreflection

Problem Statement

Let ABCABC be a triangle and DD be the midpoint of the segment BCBC. The circle that passes through DD and tangent to ABAB at BB, and the circle that passes through DD and tangent to ACAC at CC intersect at M≠DM\neq D. Let M′M' be the reflection of MM with respect to BCBC. Prove that M′M' is on ADAD.
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