# Perps in a Cyclic Quad

Geometry Level 3

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

Let $$P$$ and $$Q$$ be the points on major arc $$AD$$ satisfying $$PA=PC$$ and $$QB=QD$$.

Furthermore, let $$X$$ and $$Y$$ be the feet of the perpendiculars from $$P$$ and $$Q$$ to line $$AD$$.

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

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