Question

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

Answer 1

Answer:

Given: Two distinct circles

To prove: Two distinct circles cannot intersect each other in more than two points.

Proof: Suppose that two distinct circles intersect each other in more than two points.

∴ These points are non-collinear points.

Three non-collinear points determine one and only one circle.

∴ There should be only one circle.

This contradicts the given, which shows that our assumption is wrong.

Hence, two distinct circles cannot intersect each other in more than two points.

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