Problem 164

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Problem 164: (2021 Fall AMC 10a, 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 $C?$ $\textbf{(A) }24\pi\qquad$ $\textbf{(B) }25\pi\qquad$ $\textbf{(C) }26\pi\qquad$ $\textbf{(D) }27\pi\qquad$ $\textbf{(E) }28\pi$

Solution

Exercise 164: Solution

Isosceles triangle $ABC$ has $AB=AC=8$, and a circle of radius $12$ is tangent to line $AB$ at $B$ and line $AC$ at $C$. What is the area of the circle through $A,B,C$?

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