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Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?
To do:
We have to draw different pairs of circles and find the number of points each pair have in common and the maximum number of common points.
Solution:
(i) In the first pair, two circles do not intersect each other. Therefore they have no point in common.
(ii) In the second pair, two circles intersect (touch) each other at one point $P$. Therefore, they have one point in common.
(iii) In the third pair, two circles intersect each other at two points. Therefore, they have two points in common.
There is no other possibility of two circles intersecting each other.
Therefore, two circles have at most two points in common.
Updated on: 10-Oct-2022
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