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2 right angles, 2 centroids, 1 circumcircle given, equal angles wanted

Source: St. Petersburg 2019 10.4

May 1, 2019
geometrycircumcircleCentroidequal angles

Problem Statement

Given a convex quadrilateral ABCDABCD. The medians of the triangle ABCABC intersect at point MM, and the medians of the triangle ACDACD at pointN N. The circle, circumscibed around the triangle ACMACM, intersects the segment BDBD at the point KK lying inside the triangle AMBAMB . It is known that ∠MAN=∠ANC=90o\angle MAN = \angle ANC = 90^o. Prove that ∠AKD=∠MKC\angle AKD = \angle MKC.
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