CBSE Class 9 Answered

Suppose there are two different circles passing thru' given 3 non collinear points.

The circles be C and C'.

The centre of C is equidistant from all the three points as they are lying on the circle C.

So the centre of C, say O, lies on the perpendicular bisectors of all three line segments joining these points.

Note that every point on the perpendicular bisector is equidistant from the end points of a line segment)

So O os the point of intersection of all the three line segments.

Simliraly, we get that if O' is the centre of the circle C'  passing the the given points, then O' is also the point

of intersection of the perpendicular bisectors of all the thre line segments formed by the given three points.

So O and O' must be the same as three line segments formed by 3 non collinrear points can't meet at two different points.

So our assumption that C and C' are two different circles is incorrect.

Therefore there's one and only one circle passing through given three non collinear points.