Circles Passing Through Different Points are as follows.
Circles Passing Through One Point
If there is a point in a plane then through that point many circles can pass. We can say infinite circles can pass. We can understand it practically from the figure given below.
Circles Passing Through Two Points
If there are two points in a plane then also an infinite number of circles can pass through those two points. Here is the figure below to understand it clearly.
In the above figure, the Centre of all the circles lies on a straight line which is the perpendicular bisector of the line AB. Here, line AB is a chord.
Circles Passing Through Three Points
If there are three points and they lie on a straight line means they are collinear then we see that we can’t draw a circle that passes through all three points. In this condition, The Second or third point will lie inside or outside the circle passing through two points.
Now if we take three points that do not lie on a straight line means they are non-collinear. In this condition, only one circle can be drawn, and how, let’s see below. Let there are three points A, B, and C which are non-collinear as shown below.
Joining the three points A, B, and C and after that, if we draw perpendicular bisectors of AB and BC then both the perpendicular bisectors intersect each other at a point. If we consider this point as a Centre O and OA as a radius and draw a circle then that circle will pass through all three points. It means OA = OB = OC
It shows that all the three points are equidistant from the point O and there is only one intersecting point of both the perpendicular bisector so we can draw only one circle. Therefore, there is one and only one circle passing through three non-collinear points.