Difference between revisions of "2018 AMC 10A Problems/Problem 15"
Ishankhare (talk | contribs) (Created page with "Two circles of radius 5 are externally tangent to each other and are internally tangent to a circle of radius 13 at points <math>A</math> and <math>B</math>, as shown in the...") |
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<math>\textbf{(A) } 21 \qquad \textbf{(B) } 29 \qquad \textbf{(C) } 58 \qquad \textbf{(D) } 69 \qquad \textbf{(E) } 93 </math> | <math>\textbf{(A) } 21 \qquad \textbf{(B) } 29 \qquad \textbf{(C) } 58 \qquad \textbf{(D) } 69 \qquad \textbf{(E) } 93 </math> | ||
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| + | ==Solution== | ||
| + | |||
| + | Call the largest circle <math>\circle X</math>. | ||
Revision as of 14:47, 8 February 2018
Two circles of radius 5 are externally tangent to each other and are internally tangent to a circle of radius 13 at points 
and 
, as shown in the diagram. The distance 
can be written in the form 
, where 
and 
are relatively prime positive integers. What is 
?
![[asy] draw(circle((0,0),13)); draw(circle((5,-6.2),5)); draw(circle((-5,-6.2),5)); label("$B$", (9.5,-9.5), S); label("$A$", (-9.5,-9.5), S); [/asy]](http://latex.artofproblemsolving.com/c/1/d/c1d7b33c122356459463ccf321031d04f8f53752.png)
Solution
Call the largest circle $\circle X$ (Error compiling LaTeX. Unknown error_msg).
