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Benelux Olympiad 2020, Problem 3 (tangent circles through triangle vertices)

Source: BxMO 2020, Problem 3

May 2, 2020
geometryBxMOBenelux

Problem Statement

Let ABCABC be a triangle. The circle ωA\omega_A through AA is tangent to line BCBC at BB. The circle ωC\omega_C through CC is tangent to line ABAB at BB. Let ωA\omega_A and ωC\omega_C meet again at DD. Let MM be the midpoint of line segment [BC][BC], and let EE be the intersection of lines MDMD and ACAC. Show that EE lies on ωA\omega_A.
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