Haruki

Haruki's theorem

For two pairs of circles (a,b) and (c,d), each pair belonging to a pencil of circles orthogonal to the other pencil (one pencil being elliptic the other hyperbolic), the intersection points of the circles belong, by four, to four circles.

Look at the document Haruki2.html for another case of two parabolic pencils of circles.

http://users.math.uoc.gr/~pamfilos/