### Theory:

*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**:

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*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.