1. 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:

v) Two points in common <\tr><\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> |
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<\th> | <\th><\tr> |

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

<\th> | <\th><\tr> |