Question 90
$O$ is the center and $r$ is the radius of the incircle of a tangential quadrilateral $ABCD$. Let $P$ be the point of intersection of the lines $AB$ and $CD$, $Q$ be the point of intersection of the lines $AD$ and $BC$, and $E$ be the point of intersection of the diagonals $AC$ and $BD$. Show that $|OE| \cdot d = r^2$ where $d$ is the distance from the point $O$ to the line $PQ$.