+1678 Let $ABCD$ be a trapezoid with bases $\overline{AB}$ and $\overline{CD}.$ Let $P$ be a point on side $\overline{CD},$ and let $X,$ $Y$ be the feet of the altitudes from $P$ to $\overline{AD},$ $\overline{BC}$ respectively. Prove that if $AB= 5,$ $CD= 5,$ and $\frac{CP}{PD} = \frac{12}{24},$ then $PX = PY.$
