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Slovenia 2019 TST2 P3

Source: 2019 Slovenia 2nd TST Problem 3

February 13, 2019
Team Selection Testgeometry

Problem Statement

Let ABCABC be a non-right triangle and let MM be the midpoint of BCBC. Let DD be a point on AMAM (D≠A, D≠M). Let ω1 be a circle through DD that intersects BCBC at BB and let ω2 be a circle through DD that intersects BCBC at CC. Let ABAB intersect ω1 at BB and EE, and let ACAC intersect ω2 at CC and FF. Prove, that the tangent on ω1 at EE and the tangent on ω2 at FF intersect on AMAM.
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