+73 In parallelogram $EFGH,$ let $M$ be the midpoint of side $\overline{EF},$ and let $N$ be the midpoint of side $\overline{EH}.$ Line segments $\overline{FH}$ and $\overline{GM}$ intersect at $P,$ and line segments $\overline{FH}$ and $\overline{GN}$ intersect at $Q.$ Find $\frac{PQ}{FH}.$
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 $PX=PY.$
