Perps in a Cyclic Quad

Geometry Level 3

Let ABCDABCD be a cyclic quadrilateral with ABD=ACD>90\angle ABD = \angle ACD >90^{\circ}.

Let PP and QQ be the points on major arc ADAD satisfying PA=PCPA=PC and QB=QDQB=QD.

Furthermore, let XX and YY be the feet of the perpendiculars from PP and QQ to line ADAD.

If AB=20AB=20, CD=14CD=14, and BC=16BC=16, then find the length of XYXY.


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