# Perps in a Cyclic Quad

**Geometry**Level 4

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 \(XY\).