AMC 10 2021-fall-a Problem 15

Isosceles triangle $ABC$ has $AB = AC = 3\sqrt6$, and a circle with radius $5\sqrt2$ is tangent to line $AB$ at $B$ and to line $AC$ at $C$. What is the area of the circle that passes through vertices $A$, $B$, and $C?$ $\textbf{(A) }24\pi \textbf{(B) }25\pi \textbf{(C) }26\pi \textbf{(D) }27\pi \textbf{(E) }28\pi$