Two free circles generally intersect in two points with the exception of two cases: if the circles are tangential or if they merge. A line defined by these two points of intersection is therefore not defined in these exceptional cases, the situation becomes singular. Using non-standard analysis (NSA) and infinitesimal perturbation the first singularity can be removed continuously, the second cannot (if the circles are free).
CindyJS draws the line in (semi transpartent) black, the NSA result is drawn in red. As one can see in the tangential situation only the NSA continuation is drawn.