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Prove that any three points on a circle cannot be collinear with construction |
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Answer» Let A, B, and C be any three points on a circle. Suppose these three points A, B, and C on the collinear. Therefore, the PERPENDICULAR bisectors of the chords AB and BC must be parallel because two or more lines which are to 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,C on the circle are collinear is not correct. THUS, any three points on a circle cannot be collinear. |
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