# 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

~Punxsutawny Phil

## See also

 2021 CMC 12A (Problems • Answer Key • Resources) Preceded byProblem 1 Followed byProblem 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 (Problems • Answer Key • Resources) Preceded byProblem 1 Followed byProblem 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

The problems on this page are copyrighted by the MAC's Christmas Mathematics Competitions.