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 $$Q$$?