Question

Prove that one and only one circle can be drawn through three non collinear points .


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Answer 1

Let's proof: The point O lies on the perpendicular bisector of AB. And also, O lies on the perpendicular bisector of BC. Thus, we can say from above OA = OB = OC = r (where r stands for radius of the circle). ... Hence, there is one and only one circle passing through three non collinear points that are A, B and C.

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Answer 2

Answer:

Let's proof: The point O lies on the perpendicular bisector of AB. And also, O lies on the perpendicular bisector of BC. Thus, we can say from above OA = OB = OC = r (where r stands for radius of the circle). ... Hence, there is one and only one circle passing through three non collinear points that are A, B and C.