2021 CMC 12A Problems/Problem 2

The following problem is from both the 2021 CMC 12A #2 and 2021 CMC 10A #2, so both problems redirect to this page.

Problem

Two circles of equal radius $r$ have an overlap area of $7\pi$ and the total area covered by the circles is $25\pi$. What is the value of $r$?

$\textbf{(A) } 2\sqrt{2}\qquad\textbf{(B) } 2\sqrt{3}\qquad\textbf{(C) } 4\qquad\textbf{(D) } 5\qquad\textbf{(E) } 4\sqrt{2}\qquad$

Solution

The area of one of the circles is \[\frac{25\pi+7\pi}{2}=16\pi.\] The radius of a circle with area $16\pi$ is $\boxed{\textbf{(C) } 4}$.

Video Solution

https://www.youtube.com/watch?v=H4uIpLB-6Jo

~Punxsutawny Phil

See also

2021 CMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All CMC 12 Problems and Solutions
2021 CMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All CMC 10 Problems and Solutions

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