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Circle through a point
Given a point $$O$$, it is always possible to draw infinitely many circles through the given point.

In other words, an infinite number of circles can be drawn through a given point.

Illustration: Circle through two points
Given any two points, it is  always possible to draw infinitely many circles through the given points.

In other words, an infinite number of circles can be drawn, passing through a pair of points.

Illustration: Circle through three points
Case 1: Collinear points

If the three points are collinear, then it is impossible to draw a circle using all three points.
Any set of points are said to be collinear if all the points lie on the same line.
Illustration: Case 2: Non-collinear points

If the three points are non-collinear, then it is possible to draw only one circle using all the three points.
Any set of points are said to be non-collinear if all the points do not lie on the same line.
Illustration: Theorem: There is one and only one circle passing through three non-collinear points.