Difference between revisions of "2004 AMC 10A Problems/Problem 23"

(New page: ==Problem== Circles <math>A</math>, <math>B</math>, and <math>C</math> are externally tangent to each other and internally tangent to circle <math>D</math>. Circles <math>B</math> and <mat...)
 
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== See also ==
 
== See also ==
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=131335 AoPS topic]
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* <url>viewtopic.php?t=131335 AoPS topic</url>
 
{{AMC10 box|year=2004|ab=A|num-b=22|num-a=24}}
 
{{AMC10 box|year=2004|ab=A|num-b=22|num-a=24}}

Revision as of 16:08, 16 October 2007

Problem

Circles $A$, $B$, and $C$ are externally tangent to each other and internally tangent to circle $D$. Circles $B$ and $C$ are congruent. Circle $A$ has radius $1$ and passes through the center of $D$. What is the radius of circle $B$?

AMC10 2004A 23.png

$\mathrm{(A) \ } \frac{2}{3} \qquad \mathrm{(B) \ } \frac{\sqrt{3}}{2} \qquad \mathrm{(C) \ } \frac{7}{8} \qquad \mathrm{(D) \ } \frac{8}{9} \qquad \mathrm{(E) \ } \frac{1+\sqrt{3}}{3}$

Solution

See also

  • <url>viewtopic.php?t=131335 AoPS topic</url>
2004 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 22
Followed by
Problem 24
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All AMC 10 Problems and Solutions
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