Please refer to video for the figure of different pair of circles.
There can be three possibilities.
(i) When two circles are not touching each other, then there is no common point. So, the maximum number of common points in this case, is `0`.
(i) When two circles are just touching each other, then there is a single common point. So, the maximum number of common points in this case, is `1`.
(i) When two circles are intersecting each other, then there are two common points. So, the maximum number of common points in this case, is `2`.
