SHARYGIN 2017 Problem 22

Let $P$ be an arbitrary point on the diagonal $AC$ of cyclic quadrilateral $ABCD$ , and $PK, PL, PM, PN, PO$ be the perpendiculars from $P$ to $AB, BC, CD, DA, BD$ respectively. Prove that the distance from $P$ to $KN$ is equal to the distance from $O$ to $ML$ .