Question

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

Answer:

two different circles cannot intersect each other at more than

two points.

Explanation:

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.

Answer 2

Answer:

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