2006 AIME I Problems/Problem 10

Revision as of 09:46, 23 August 2006 by JBL (talk | contribs)

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 $a^2+b^2+c^2.$



An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.



Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.


See also