Find a circle that passes exactly through seven points of the plane (no more, no less) with integer coordinates.

Wrote up a quick program that found the following:

The circle passing through the following 7 integer lattice points passes through no others:

(0,0)
(11,2)
(-11,2)
(30,40)
(-30,40)
(25,50)
(-25,50)

Note that this circle is given by the equation x^2+(y-r)^2 = r^2 with r=125/4.

Posted by David Shin on 2004-08-19 14:12:44