2019 AIME II Problem 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 \tfrac{m}{n}, where m and n are relatively prime positive 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.