Let \(ABCD\) be a trapezoid with bases \(\overline{AB}\) and \(\overline{CD}.\) Let \(AD=5\) and \(BC=7\) and let \(P\) be a point on side \(\overline{CD}\) such that \(\frac{CP}{PD}=\frac{7}{5}.\) Let \(X,Y\) be the feet of the altitudes from \(P\) to \(\overline{AD},\)\(\overline{BC}\) respectively. Show that \(PX=PY.\)
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