Question
Prove that two different circles cannot intersect each other at more than two points.
✓
Answer
Suppose two circles intersect in three points $A, B, C$.
Then $A, B, C$ are non-collinear so a unique circle passes through these three points.
This is contradiction to the face that two given circles are passing through $A, B, C$.
Hence, two circles cannot intersect each other at more than two points.
Then $A, B, C$ are non-collinear so a unique circle passes through these three points.
This is contradiction to the face that two given circles are passing through $A, B, C$.
Hence, two circles cannot intersect each other at more than two points.
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