Question

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

Answer 1

Step-by-step explanation:

Given :-

In a circle with center O points A, B and C are any 3 points on the circle.

To Prove :-

points A, B, C cannot be collinear.

Proof :-

seg AB and seg BC are drawn.

Let point A, B, C are collinear point

∴ Perpendicular bisector of seg AB and seg BC parallel to each other.

∴ They will never intersect each other.

∴ There will be no point in their plane which is equidistant from points A, B, C.

But, Point O is equidistant from points A, B, C because it's the centre of the circle.

But, This is a contradiction.

∴ Our assumption is wrong.

∴ points A, B, C are not collinear.

∴ points A, B, C cannot be collinear.

∴ Any three points on a circle cannot be collinear this property is proved.