Draw different pairs of circles. How many points does each pair have in common?
what is the maximum number of common points?

Different pairs of circles are as follows:

i) No points in common (externally)	(ii) One point in common (internally)
iii) No points in common (internally)	iv) One point in common (externally)
v) Two points in common

From figures, it is obvious that these pairs many have 0 or 1 or 2 points in common.

Hence, a pair of circles cannot intersect each other at more than two points.