Circumscribed quadrilateral

Geometry Level 4

Quadrilateral ABCDABCD is circumscribed about a circle II, that is tangent to AB,BC,CD,DAAB, BC, CD, DA at E,F,G,H,E, F, G, H, respectively. Suppose that ACAC and BDBD intersect at point PP and EGEG and FHFH intersect at point QQ. If AB=5,BC=6,CD=8,DA=7AB=5, BC=6, CD=8, DA=7, what is the distance between PP and Q?Q?

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