Problem

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Tags: geometry, parallelogram, circumcircle, Euler, geometric transformation



Let $ABCD$ is a cyclic. $K,L,M,N$ are midpoints of segments $AB$, $BC$ $CD$ and $DA$. $H_{1},H_{2},H_{3},H_{4}$ are orthocenters of $AKN$ $KBL$ $LCM$ and $MND$. Prove that $H_{1}H_{2}H_{3}H_{4}$ is a paralelogram.