2021 Fall AMC 10A 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\qquad\textbf{(B) }25\pi\qquad\textbf{(C) }26\pi\qquad\textbf{(D) }27\pi\qquad\textbf{(E) }28\pi

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.