Question 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 $\frac{m}{n},$ where $m$ and $n$ are relatively prime integers. Find $m+n.$