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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