Difference between revisions of "2016 AIME I Problems/Problem 14"
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Revision as of 17:10, 4 March 2016
Problem
Centered at each lattice point in the coordinate plane are a circle radius and a square with sides of length
whose sides are parallel to the coordinate axes. The line segment from
to
intersects
of the squares and
of the circles. Find
.
Solution
First note that and
so every point of the form
is on the line. Then consider the line
from
to
. Translate the line
so that
is now the origin.