2021 AMC 10B Problems/Problem 7

Problem

In a plane, four circles with radii $1,3,5,$ and $7$ are tangent to line $l$ at the same point $A,$ but they may be on either side of $l$ . Region $S$ consists of all the points that lie inside exactly one of the four circles. What is the maximum possible area of region $S$ ?

$\textbf{(A) }24\pi \qquad \textbf{(B) }32\pi \qquad \textbf{(C) }64\pi \qquad \textbf{(D) }65\pi \qquad \textbf{(E) }84\pi$

Solution

D

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2021 AMC 10B Problems/Problem 7

Problem

Solution