Q. 113.8( 16 Votes )

Prove that two different circles cannot intersect each other at more than two points.

Answer :

Let two different circles intersect at three distinct points A, B and C.


Then, these points are already non-collinear.


A unique circle can be drawn to pass through these points. This is a contradiction.


Hence, two different circles cannot intersect each other at more than two points.


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