2020 OIM Problems/Problem 6

Problem

Let $ABC$ be an acute and scalene triangle. Let $H$ be the orthocenter and $O$ the circumcenter of triangle $ABC$, and let $P$ be an interior point of the segment $HO$. The circumference with center $P$ and radius $PA$ again intersects the lines $AB$ and $AC$ at points $R$ and $S$, respectively. We denote by $Q$ the point symmetrical to point $P$ with respect to the bisector of $BC$. Prove that the points $P$, $Q$, $R$ and $S$ belong to the same circle.

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

Solution

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See also

OIM Problems and Solutions