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Found problems: 1

2018 Middle European Mathematical Olympiad, 5
Tags: parallelogram , geometry , ohm
Let $ABC$ be an acute-angled triangle with $AB<AC,$ and let $D$ be the foot of its altitude from$A,$ points $B'$ and $C'$ lie on the rays $AB$ and $AC,$ respectively , so that points $B',$ $C'$ and $D$ are collinear and points $B,$ $C,$ $B'$ and $C'$ lie on one circle with center $O.$ Prove that if $M$ is the midpoint of $BC$ and $H$ is the orthocenter of $ABC,$ then $DHMO$ is a parallelogram.