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<DKL=<CLK if <BMN=<MNC, midpoints of cyclic (2011 Kyiv City MO 9.4)

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July 14, 2020
geometryCyclicequal anglesmidpoints

Problem Statement

Let ABCDABCD be an inscribed quadrilateral. Denote the midpoints of the sides AB,BC,CDAB, BC, CD and DADA through M,L,NM, L, N and KK, respectively. It turned out that ∠BMN=∠MNC\angle BM N = \angle MNC. Prove that: i) ∠DKL=∠CLK\angle DKL = \angle CLK. ii) in the quadrilateral ABCDABCD there is a pair of parallel sides.
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