KöMaL problem A, 2026

Call four points to be in general position if they are pairwise distinct, no three of them are collinear, and no two of the six lines determined by them are parallel. Let $A$, $B$, $C$, $D$ be points in general position lying on a circle. Let $E$ be the intersection point of lines $AB$ and $CD$, let $F$ be the intersection point of lines $AC$ and $BD$, and let $G$ be the intersection point of lines $AD$ and $BC$. In triangle $EFG$, denote by $P$, $Q$, and $R$ the feet of the altitudes corresponding to the vertices $E$, $F$, and $G$, respectively.