2014 OIM Problems/Problem 5

Problem

Let $ABC$ be an acute triangle and $H$ be the point of intersection of the heights. The height from $A$ cuts $BC$ in $D$. Let $M$ and $N$ be the midpoints of $BH$ and $CH$, respectively. $DM$ and $DN$ intersect $AB$ and $AC$ at $X$ and $Y$, respectively. If $XY$ intersects $BH$ at $P$ and $CH$ in $Q$, show that $H, P, D$, and $Q$ are on the same circle.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions