Difference between revisions of "2006 AMC 10A Problems/Problem 16"

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== Problem ==
 
== Problem ==
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A circle of radius 1 is tangent to a circle of radius 2. The sides of <math>\triangle ABC</math> are tangent to the circles as shown, and the sides <math>\overline{AB}</math>  and <math>\overline{AC}</math>  are congruent. What is the area of <math>\triangle ABC</math>?
 
A circle of radius 1 is tangent to a circle of radius 2. The sides of <math>\triangle ABC</math> are tangent to the circles as shown, and the sides <math>\overline{AB}</math>  and <math>\overline{AC}</math>  are congruent. What is the area of <math>\triangle ABC</math>?
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<math>\mathrm{(A) \ } \frac{35}{2}\qquad\mathrm{(B) \ } 15\sqrt{2}\qquad\mathrm{(C) \ } \frac{64}{3}\qquad\mathrm{(D) \ } 16\sqrt{2}\qquad\mathrm{(E) \ } 24\qquad</math>
 
<math>\mathrm{(A) \ } \frac{35}{2}\qquad\mathrm{(B) \ } 15\sqrt{2}\qquad\mathrm{(C) \ } \frac{64}{3}\qquad\mathrm{(D) \ } 16\sqrt{2}\qquad\mathrm{(E) \ } 24\qquad</math>
 
== Solution ==
 
== Solution ==
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== See Also ==
 
== See Also ==
*[[2006 AMC 10A Problems]]
 
 
*[[2006 AMC 10A Problems/Problem 15|Previous Problem]]
 
  
*[[2006 AMC 10A Problems/Problem 17|Next Problem]]
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* [[2006 AMC 10A Problems]]
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* [[2006 AMC 10A Problems/Problem 15|Previous Problem]]
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* [[2006 AMC 10A Problems/Problem 17|Next Problem]]
  
 
[[Category:Introductory Geometry Problems]]
 
[[Category:Introductory Geometry Problems]]

Revision as of 23:10, 5 September 2006

Problem


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A circle of radius 1 is tangent to a circle of radius 2. The sides of $\triangle ABC$ are tangent to the circles as shown, and the sides $\overline{AB}$ and $\overline{AC}$ are congruent. What is the area of $\triangle ABC$?

$\mathrm{(A) \ } \frac{35}{2}\qquad\mathrm{(B) \ } 15\sqrt{2}\qquad\mathrm{(C) \ } \frac{64}{3}\qquad\mathrm{(D) \ } 16\sqrt{2}\qquad\mathrm{(E) \ } 24\qquad$

Solution

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