Prove that two circles cannot intersect at mo | vedclass

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(N/A) Assume that two circles intersect at three distinct points,$A$,$B$,and $C$. Since $A$,$B$,and $C$ are three distinct points,they are non-colline

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(N/A) Assume that two circles intersect at three distinct points,$A$,$B$,and $C$.
Since $A$,$B$,and $C$ are three distinct points,they are non-collinear.
According to the geometric theorem,there is one and only one circle that passes through three non-collinear points.
Therefore,if two circles pass through the same three points $A$,$B$,and $C$,they must be the same circle.
This contradicts the assumption that there are two distinct circles.
Hence,it is impossible for two distinct circles to intersect at more than two points.

Prove that two circles cannot intersect at more than two points.

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