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Question

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

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Solution

To prove: Two different circles cannot intersect each other at more than two points.

Construction: Let two circles intersect each other at three points A,B and C

Proof :

Since two circles with centres O and O intersect at A,B and C.

A,B and C are non-collinear points

Circle with centre O passes through three points A,B and C.

and circle with centre O also passes through three points A,B and C.

But one and only one circle can be drawn through three points

Our supposition is wrong

Two circle cannot intersect each other not more than two points.

Observe the following figure,



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