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?

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

The centers of these circles form a 3-4-5 triangle, which has an area equal to 6.

The 3 triangles determined by one vertex (one center) and two tangent points closest it

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