Question

1. Find the locus of the centre of a circle passing through three given points A, B
and C which are non-collinear​

Answer 1

Answer:

Let A,B and C be three non-collinear points

Join AB and BC

Draw perpendicular bisector of AB and BC

Let them meet at point O

Then O lie on the right bisector of AB

So, OA=OB

And O lies on the right bisector of BC

So, OB=OC

Hence, the point O is equidistant from A,B and C.

Now since the right bisector of AB and BC are non-parallel lines, therefore they have only one point in common.

So, O is the only point equidistant from A,B and C.

Hence, the required locus is the centre of the circle through the given non-collinear points.

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