Suppose A B C is a triangle, and define B_{1} and C_{1} such that \triangle A B_{1} C and \triangle A C_{1} B are isosceles right triangles on the exterior of \triangle A B C with right angles at B_{1} and C_{1}, respectively. Let M be the midpoint of \overline{B_{1} C_{1}}; if B_{1} C_{1}=12, B M=7 and C M=11, what is the area of \triangle A B C ?