限制quadrilateral

Quadrilateral $ABCD$is circumscribed about a circle $I$, that is tangent to $AB, BC, CD, DA$at $E, F, G, H,$respectively. Suppose that $AC$and $BD$intersect at point $P$and $EG$and $FH$intersect at point $Q$. If $AB=5, BC=6, CD=8, DA=7$, what is the distance between $P$and $Q?$