Difference between revisions of "2006 AIME I Problems/Problem 10"

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== Solution ==
 
== Solution ==
 
{{solution}}
 
{{solution}}
 
The equation of the line turns out to be <math>\displaystyle 3x=y+3</math>, so the solution is <math>9+9+1=019</math>.
 
  
 
== See also ==
 
== See also ==

Revision as of 15:47, 12 March 2007

Problem

Eight circles of diameter 1 are packed in the first quadrant of the coordinte plane as shown. Let region $\mathcal{R}$ be the union of the eight circular regions. Line $l,$ with slope 3, divides $\mathcal{R}$ into two regions of equal area. Line $l$'s equation can be expressed in the form $ax=by+c,$ where $a, b,$ and $c$ are positive integers whose greatest common divisor is 1. Find $a^2+b^2+c^2.$


2006AimeI10.PNG


Solution

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See also

2006 AIME I (ProblemsAnswer KeyResources)
Preceded by
Problem 9
Followed by
Problem 11
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions