2019 AIME II Problem 1

Points C \neq D lie on the same side of line A B so that \triangle A B C and \triangle B A D are congruent with A B=9, B C= A D=10, and C A=D B=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.