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Question
Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?
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Solution
Consider the following pair of circles :
The above circles do not intersect each other at any point. Therefore, they do not have any point in common.
The above circles touch each other internally only at one point Y. Therefore, the circles have 1 point in common.
The above circles touch each other externally only at 1 point X. Therefore, the circles have 1 point in common.
The above circles intersect each other at two points G and H. Therefore, the circles have two points in common.
It can be observed that the maximum number of common points is 2.
The above circles do not intersect each other at any point. Therefore, they do not have any point in common.
The above circles touch each other internally only at one point Y. Therefore, the circles have 1 point in common.
The above circles touch each other externally only at 1 point X. Therefore, the circles have 1 point in common.
The above circles intersect each other at two points G and H. Therefore, the circles have two points in common.
It can be observed that the maximum number of common points is 2.
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