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Easy Problem 1 Geometry

Source: IMEO 2019, Problem 1

October 14, 2019
geometrygeometry proposedgeometry solvedparallelogramhumpty pointhumpty pointslengths

Problem Statement

Let ABCABC be a scalene triangle with circumcircle ω\omega. The tangent to ω\omega at AA meets BCBC at DD. The AA-median of triangle ABCABC intersects BCBC and ω\omega at MM and NN, respectively. Suppose that KK is a point such that ADMKADMK is a parallelogram. Prove that KA=KNKA = KN.
Proposed by Alexandru Lopotenco (Moldova)
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