Question -
Answer -
We have to prove that two different circles cannot intersect each other at more than two points.
Let the two circles intersect in three points A, B and C.
Then as we know that these three points A, B and C are non-collinear. So, a unique circle passes through these three points.
This is a contradiction to the fact that two given circles are passing through A, B, C.
Hence, two circles cannot intersect each other at more than two points.
Hence, proved.