Question

prove that any shree point on a circle van not be collinear
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Answer 1

Step-by-step explanation:

Given: A circle with centre O. Points A, B and C lie on the circle. To prove: Points A, B and C are not collinear. Proof: OA = OB [Radii of the same circle] ∴ Point O is equidistant from the endpoints A and B of seg AB. ∴ Point O lies on the perpendicular bisector of AB. [Perpendicular bisector theorem] Similarly, we can prove that, Point O lies on the perpendicular bisector of BC. ∴ Point O is the point of intersection of perpendicular bisectors of AB and BC (i.e., circumcentre of ∆ABC) ……… (i) Now, suppose that the points A, B, C are collinear. Then, the perpendicular bisector of AB and BC will be parallel. [Perpendiculars to the same line are parallel] ∴ The perpendicular bisector do not intersect at O. This contradicts statement (i) that the perpendicular bisectors intersect each other at O. ∴ Our supposition that A, B, C are collinear is false. ∴ Points A, B and C are non collinear points.Read more on Sarthaks.com - https://www.sarthaks.com/854600/prove-that-any-three-points-on-a-circle-cannot-be-collinear

Answer 2

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