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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