1993 AIME Problem 15

Let \overline{CH} be an altitude of \triangle ABC. Let R\, and S\, be the points where the circles inscribed in the triangles ACH\, and BCH^{}_{} are tangent to \overline{CH}. If AB = 1995\,, AC = 1994\,, and BC = 1993\,, then RS\, can be expressed as m/n\,, where m\, and n\, are relatively prime integers. Find m + n\,.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.