Difference between revisions of "2006 AIME I Problems/Problem 10"
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== Problem == | == Problem == | ||
Eight circles of diameter 1 are packed in the first quadrant of the coordinte plane as shown. Let region <math> \mathcal{R} </math> be the union of the eight circular regions. Line <math> l, </math> with slope 3, divides <math> \mathcal{R} </math> into two regions of equal area. Line <math> l </math>'s equation can be expressed in the form <math> ax=by+c, </math> where <math> a, b, </math> and <math> c </math> are positive integers whose greatest common divisor is 1. Find <math> a^2+b^2+c^2. </math> | Eight circles of diameter 1 are packed in the first quadrant of the coordinte plane as shown. Let region <math> \mathcal{R} </math> be the union of the eight circular regions. Line <math> l, </math> with slope 3, divides <math> \mathcal{R} </math> into two regions of equal area. Line <math> l </math>'s equation can be expressed in the form <math> ax=by+c, </math> where <math> a, b, </math> and <math> c </math> are positive integers whose greatest common divisor is 1. Find <math> a^2+b^2+c^2. </math> | ||
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== Solution == | == Solution == | ||
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== See also == | == See also == | ||
| − | * [[2006 AIME I]] | + | * [[2006 AIME I Problems]] |
Revision as of 11:14, 30 June 2006
Problem
Eight circles of diameter 1 are packed in the first quadrant of the coordinte plane as shown. Let region 
be the union of the eight circular regions. Line 
with slope 3, divides into two regions of equal area. Line 
's equation can be expressed in the form 
where 
and 
are positive integers whose greatest common divisor is 1. Find 
