Difference between revisions of "2011 AMC 12A Problems/Problem 17"

Revision as of 21:20, 11 February 2011

Circles with radii $1$ , $2$ , and $3$ are mutually externally tangent. What is the area of the triangle determine by the points of tangency?

$\textbf{(A)}\ \frac{3}{5} \qquad \textbf{(B)}\ \frac{4}{5} \qquad \textbf{(C)}\ 1 \qquad \textbf{(D)}\ \frac{6}{5} \qquad \textbf{(E)}\ \frac{4}{3}$

2011 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 16	Followed by Problem 18
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 AMC 12 Problems and Solutions

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 == Solution ==
-Area of the triangle
-<math> = \frac{1}{2} \times 4 \times 3 -  \frac{1}{2} \times 1 \times 1 -  \frac{1}{2} \times 3 \times 3 \times \frac{3}{5} -  \frac{1}{2} \times 2 \times 2 \times \frac{4}{5} </math>
-<math> = \frac{6}{5} </math>
 == See also ==
 {{AMC12 box|year=2011|num-b=16|num-a=18|ab=A}}