Question

Prove that two different circle cannot intersect each other more than two point

Answer 1

Let us consider that 2 distinct circles intersect at more than 2 points.

∴These points are non-collinear points.

As 3 non-collinear points determine one and only one circle

∴There should be only one circle.
(i.e. those circles are supposed to superimpose each other)
But, the superimposition of 2 circles of different radii is impossible, i.e. concentric circles would be derived instead.

This contradicts our assumption. Therefore, our assumption is wrong.

Hence, 2 circles cannot intersect each other at more than 2 points.