Challenge · Medium problem

Trapezoid $ABCD$ has $\overline{AB}\parallel\overline{CD}$ with $AB=8$ and $CD=18$. The diagonals meet at $P$. Find the length of the segment through $P$ parallel to the bases whose endpoints lie on the legs $\overline{AD}$ and $\overline{BC}$.

Express your answer as a common fraction.