Your fact probably doesn't have a name. But a good statement would be that a quadratic polynomial has at most two roots. To see this, suppose that the two circ

Your fact probably doesn't have a name. But a good statement would be that a quadratic polynomial has at most two roots. To see this, suppose that the two circles are (x-a)^2 + (y-b)^2 = r and (x-c)^2 + (y-d)^2 = R. Subtracting gives an equation of the form (linear function in x and y) = r - R. This means that y is a linear function of x, and so we can use this to substitute in the equation for the first circle to get something of the form (quadratic function in x) = r. Then as there are at most 2 solutions for x, and each gives the corresponding solution for y, we see that two distinct circles intersect in at most 2 points.