Prove that two different circles cannot intersect each other at more than two points - Maths - Circles

Question

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

ramandeep.singh · Accepted Answer

Suppose 2 distinct circles intersect at more than 2 points
âˆ´These points are non-collinear points
As 3 non-collinear points determine one and only one circle,
âˆ´There should be only one circle
This contradicts our assumption Therefore, our assumption is
wrong
Hence, 2 circles can't intersect each other at more than 2
points

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