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This is not ISL 2005 G5

Source: Moldova TST 2019

March 10, 2019
geometry

Problem Statement

Point HH is the orthocenter of the scalene triangle ABC.ABC. A line, which passes through point HH, intersect the sides ABAB and ACAC at points DD and EE, respectively, such that AD=AE.AD=AE. Let MM be the midpoint of side BC.BC. Line MHMH intersects the circumscribed circle of triangle ABCABC at point KK, which is on the smaller arc ABAB. Prove that Nibab can draw a circle through A,D,EA, D, E and K.K.