Perps in a Cyclic Quad

Geometry Level 4

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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