Prove that two different circles cannot intersect each other at m… - Vidyadip

Question

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

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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.
$\therefore$ These points are non-collinear points. Three non-collinear points determine one and only one circle.
$\therefore$ 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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