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parallelogram on side of a triangle, concurrent lines wanted

Source: 2019 Oral Moscow Geometry Olympiad grades 8-9 p2

May 21, 2019
geometryparallelogramconcurrencyconcurrent

Problem Statement

On the side ACAC of the triangle ABCABC in the external side is constructed the parallelogram ACDEACDE . Let OO be the intersection point of its diagonals, NN and KK be midpoints of BC and BA respectively. Prove that lines DK,ENDK, EN and BOBO intersect at one point.
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