Question

prove that two different circles can't intesect each other at more than two point​

Answer 1

Answer:

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.