Question

Prove that two different circles cannot intersect each other at more than two points.
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Answer 1

Answer:

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Answer 2

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Suppose 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.