posted by jenny .
Let ABC be a triangle in the plane. Find circles C0;C1; : : : ;C6 such that Cj
has exactly j points in common with the boundary of ABC (this \boundary"
consists of the line segments AB, BC, CA). Is it possible to nd a circle C7
with 7 points in common with the boundary of ABC?
(Just use trial and error for this question - draw lots of circles and triangles
how do I do this?