Circumscribed quadrilateral

Geometry Level 4

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 $Q?$