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

(Solution)
(Solution)
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== Solution ==
 
== Solution ==
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The centers of these circles form a 3-4-5 triangle, which has an area equal to 6.
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The 3 triangles determined by one vertex (one center) and two tangent points closest it
  
 
== See also ==
 
== See also ==
 
{{AMC12 box|year=2011|num-b=16|num-a=18|ab=A}}
 
{{AMC12 box|year=2011|num-b=16|num-a=18|ab=A}}

Revision as of 22:33, 11 February 2011

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

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

See also

2011 AMC 12A (ProblemsAnswer KeyResources)
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