Assume that there are two distinct circles with centres C and D respectively.
I feel that these two circles can intersect at two points but I don't know how to prove that they can intersect at two points!
However I tried to prove it by construction like this- "I firstly construct a circle and then I again construct other circle with a compass such that they both intersect each other at two points."
Is my way of proving correct?
If not,then please provide an appropriate proof for this?
THANKS!
[Math] How should we prove that two circles can intersect at two points( at least)
circles
Best Answer
The key point to a proof is that if you have three non-collinear points, they determine a unique circle. (So two distinct circles can intersect in at most two points.) You can prove this by construction: The center of the circle will be the intersection of the perpendicular bisectors of the segments joining pairs of the points.