Circumscribed quadrilateral

Geometry Level 5

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 \(Q\)?

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