2011 AMC 12A Problems/Problem 17

Problem

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

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

Solution

Area of the triangle

$= \frac{1}{2} \times 4 \times 3 - \frac{1}{2} \times 1 \times 1 - \frac{1}{2} \times 3 \times 3 \times \frac{3}{5} - \frac{1}{2} \times 2 \times 2 \times \frac{4}{5}$

$= \frac{6}{5}$

2011 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 16	Followed by Problem 18
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2011 AMC 12A Problems/Problem 17

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