Question

prove that any three points on a circle cannot be collinear​

Answer 1

Answer:

because if points are collinear that is impossible to make a circle so three non collinear point make a circle

Answer 2

Answer:

Let A, B and C be any three points on a circle. Suppose these three points A, B and C on the circle are collinear. Therefore, the perpendicular bisectors of the chords AB and BC must be parallel because two or more lines which are perpendicular to a given line are parallel to each other. Now, AB and BC are the chords of the circle. We know that the perpendicular bisector of the chord of a circle passing through its centre. So, the perpendicular bisectors of the chords AB and BC must intersect at the centre of the circle. This is a contradiction to our statement that the perpendicular bisectors of AB and BC must be parallel, as parallel lines do not intersect at a point. Hence, our assumption that three points A, B and C on the circle are collinear is not correct. Thus, any three points on a circle cannot be collinear.

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