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 == | ||
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| − | *[[2006 AMC 10A Problems/Problem 17|Next Problem]] | + | * [[2006 AMC 10A Problems]] |
| + | * [[2006 AMC 10A Problems/Problem 15|Previous Problem]] | ||
| + | * [[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 
are tangent to the circles as shown, and the sides 
and 
are congruent. What is the area of ?
Solution
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