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Prove that two different circles cannot intersect each other at more than two points.
To do:
We have to prove that two different circles cannot intersect each other at more than two points.
Solution:
Let two circles intersect each other at three points $A, B$ and $C$
Two circles with centres $O$ and $O’$ intersect at $A, B$ and $C$
This implies,
$A, B$ 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 $C$
One and only one circle can be drawn through three points.
Therefore, our supposition is wrong
Two circles cannot intersect each other not more than two points.
Updated on: 10-Oct-2022
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