KöMaL problem A, 2021

Geometry Difficulty 7.0 National Olympiad, round 2 Prove it Hungary

Let $ABCD$ be a cyclic quadrilateral. Let lines $AB$ and $CD$ intersect in $P$ , and lines $BC$ and $DA$ intersect in $Q$ . The feet of the perpendiculars from $P$ to $BC$ and $DA$ are $K$ and $L$ , and the feet of the perpendiculars from $Q$ to $AB$ and $CD$ are $M$ and $N$ . The midpoint of diagonal $AC$ is $F$ .

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