Given a quadrilateral $ABCD$ simultaneously inscribed and circumscribed, assume that none of its diagonals or sides is a diameter of the circumscribed circle. Let $P$ be the intersection point of the external bisectors of the angles near $A$ and $B$. Similarly, let $Q$ be the intersection point of the external bisectors of the angles $C$ and $D$. If $J$ and $O$ respectively are the incenter and circumcenter of $ABCD$ prove that $OJ\perp PQ$.