Question 165
In the trapezoid $ABCD$ with perpendicular diagonals, the points $P$, $N$, $Q$, $M$ are the midpoints of the sides $AB$, $BC$, $CD$, $DA$ respectively. On the base $CD$ there is a point $L$ (different from the point $Q$) for which the angle $MLN$ is a right angle. Find the angle $LPA$.
(Bogdan Rublyov)
(Bogdan Rublyov)