Question 1
Two different points, $C$ and $D,$ lie on the same side of line $AB$ so that $\triangle ABC$ and $\triangle BAD$ are congruent with $AB = 9,$ $BC = AD = 10,$ and $CA = DB = 17.$ The intersection of these two triangular regions has area $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$