counting circles in a grid
Source:
November 15, 2009
Problem Statement
The figure below is a grid of points.
[asy]unitsize(15);
for ( int x = 1; x <= 4; ++x )
for ( int y = 1; y <= 4; ++y )
dot((x, y));[/asy]Each pair of horizontally adjacent or vertically adjacent points are distance 1 apart. In the plane of this grid, how many circles of radius 1 pass through exactly two of these grid points?