Question 97
Let $ABTCD$ be a convex pentagon with area $22$ such that $AB = CD$ and the circumcircles of triangles $TAB$ and $TCD$ are internally tangent. Given that $\angle ATD = 90^{\circ}$, $\angle BTC = 120^{\circ}$, $BT = 4$, and $CT = 5$, compute the area of triangle $TAD$.