Question 83
Points $B$ and $C$ are chosen on the circle with diameter $AD$ in such a way that $AB = AC$. Point $P$ is an arbitrary point of the segment $BC$, and points $M$ and $N$ are chosen on the segments $AB$ and $AC$ respectively in such a way that $PMAN$ is a parallelogram. Let $PL$ be a bisector in triangle $MPN$. Line $PD$ intersects $MN$ in point $Q$. Prove that points $B$, $Q$, $L$, and $C$ are cyclic.
(Mykhaylo Plotnikov, Danylo Khilko)
(Mykhaylo Plotnikov, Danylo Khilko)