Difference between revisions of "2006 AMC 12A Problems/Problem 19"
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Circles with centers <math>(2,4)</math> and <math>(14,9)</math> have radii <math>4</math> and <math>9</math>, respectively. The equation of a common external tangent to the circles can be written in the form <math>y=mx+b</math> with <math>m>0</math>. What is <math>b</math>? | Circles with centers <math>(2,4)</math> and <math>(14,9)</math> have radii <math>4</math> and <math>9</math>, respectively. The equation of a common external tangent to the circles can be written in the form <math>y=mx+b</math> with <math>m>0</math>. What is <math>b</math>? | ||
| − | <math> \mathrm{(A) \ } \frac{908}{199}\qquad \mathrm{(B) \ } \frac{909}{119}\qquad \mathrm{(C) \ } \frac{130}{17}\qquad \mathrm{(D) \ } \frac{911}{119} | + | <math> \mathrm{(A) \ } \frac{908}{199}\qquad \mathrm{(B) \ } \frac{909}{119}\qquad \mathrm{(C) \ } \frac{130}{17}\qquad \mathrm{(D) \ } \frac{911}{119}</math><math>\mathrm{(E) \ } \frac{912}{119}</math> |
== Solution == | == Solution == | ||
Revision as of 23:03, 10 July 2006
Problem
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Circles with centers 
and 
have radii 
and 
, respectively. The equation of a common external tangent to the circles can be written in the form 
with 
. What is 
?
