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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