Question

Prove that two different circles cannot intersect each other at more than two points....Explain it nicely or on paper

Answer 1

 Let 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.

This contradicts our assumption. Therefore,

 our assumption is wrong.

Hence, 2 circles can't intersect each other at more than 2 points.

I hope this is enough?