1993 AIME Problem 15

Let \overline{C H} be an altitude of \triangle A B C. Let R and S be the points where the circles inscribed in triangles ACH and \mathrm{BCH} are tangent to \overline{C H}. If A B=1995, A C=1994, and B C=1993, then R S can be expressed as m/n, where m and n are relatively prime positive integers. Find m+n.