SHARYGIN 2014 Problem 24

A circumscribed pyramid $ABCDS$ is given. The opposite sidelines of its base meet at points $P$ and $Q$ in such a way that $A$ and $B$ lie on segments $PD$ and $PC$ respectively. The inscribed sphere touches faces $ABS$ and $BCS$ at points $K$ and $L$ . Prove that if $PK$ and $QL$ are complanar then the touching point of the sphere with the base lies on $BD$ .