Difference between revisions of "2021 CMC 12A Problems/Problem 2"

Latest revision as of 20:48, 3 January 2021

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

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 $r$ ?

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

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 $\boxed{\textbf{(C) } 4}$ .

~Punxsutawny Phil

2021 CMC 12A (Problems • Answer Key • Resources)
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 (Problems • Answer Key • Resources)
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

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

@@ Line 7: / Line 7: @@
 ==Solution==
 The area of one of the circles is <cmath>\frac{25\pi+7\pi}{2}=16\pi.</cmath> The radius of a circle with area <math>16\pi</math> is <math>\boxed{\textbf{(C) } 4}</math>.
+==Video Solution==
+https://www.youtube.com/watch?v=H4uIpLB-6Jo
+~Punxsutawny Phil
 ==See also==