Apollonius circles in the CCP case
the given point and circles are red; drag the red point and the four black points to change the CCP configuration
if the red point is outside the red circles or inside their intersection then the solution is given by the green Apollonius circles; their points of intersection and the external (and blue) center of similitude of the given circles are collinear
if the red point is inside one of the red circles and outside the other then the solution is given by the purple Apollonius circles; their points of intersection and the internal (and yellow) center of similitude of the given circles are collinear