Geometry

In right triangle ABC, \angle ACB = 90^\circ, and the legs are a = BC and b = AC.  Let $S$ and $T$ be points on $\overline{AC}$ and $\overline{BC},$ respectively.  Let $R$ be the foot of the altitude from $S$ to $\overline{AB},$ and let $U$ be the foot of the altitude from $T$ to $\overline{AB}.$  Find the smallest possible value of RU