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Balkan TSTp3.2

Source: Azerbaijan Balkan TST 2016 no 3

October 20, 2016
geometry

Problem Statement

İn triangle ABCABC the bisector of ∠BAC\angle BAC intersects the side BCBC at the point DD.The circle ω\omega passes through AA and tangent to the side BCBC at DD.ACAC and ω\omega intersects at MM second time , BMBM and ω\omega intersects at PP second time. Prove that point PP lies on median of triangle ABDABD.
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