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

Posted by Chunna Bhokta 3 years, 11 months ago

CBSE > Class 09 > Mathematics

3 answers

Merina Tuzzahan 3 years, 11 months ago

Thanks

1Thank You

Deekshith Ka 3 years, 11 months ago

25-53+49

2Thank You

Gaurav Seth 3 years, 11 months ago

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.

2Thank You

ANSWER

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CBSE > Class 09 > Mathematics