MathDB
cyclic wanted, 2 circles related

Source: Balkan MO Shortlist 2013 G5 BMO

March 3, 2020
geometryCyclicConcycliccircles

Problem Statement

Let ABCABC be an acute triangle with AB<AC<BCAB < AC < BC inscribed in a circle (c)(c) and let EE be an arbitrary point on its altitude CDCD. The circle (c1)(c_1) with diameter ECEC, intersects the circle (c)(c) at point KK (different than CC), the line ACAC at point LL and the line BCBC at point MM. Finally the line KEKE intersects ABAB at point NN. Prove that the quadrilateral DLMNDLMN is cyclic.
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