there is one and only one circle that can passing non-conical point? proof
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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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