Question 27
Points $A$, $B$, $C$, $M$ are such that $B$, $M$, $C$ lie on a line, $AB = AC = 353$, and $BM = MC$. Point $I$ is on segment $AM$ such that the circle centered at $I$ through $M$ has radius $106$ and is tangent to $AB$ and $AC$. Given that there are two possible areas of right triangle $AMB$, find the larger one.