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

Different pairs of circles are as follows:

v) Two points in common <\tr>image<\tr><\table>
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.

i) No points in common (externally) <\th>(ii) One point in common (internally)<\th><\tr>
image<\th>image<\th><\tr>
iii) No points in common (internally)<\th>iv) One point in common (externally)<\th><\tr>
image<\th>image<\th><\tr>