☼ Circle  :  The set of all the points of a plane, at a given distance from a given point of the plane, is called a circle. The given point is called the centre of the circle and the given distance is called the radius of the circle.
In the given figure, P is the centre and  r  is the radius.

A circle with centre P and radius  r is denoted by  ⊙ ( P, r ).

 If   P   is   a   point  of  a  plane    and  r  is  a  positive  real  number  then   ⊙ (P, r)   =    { A / PA  =  r  and  A    }. We shall call the plane  as the plane of  the  ⊙ (P, r).

The relation between  ⊙ (P, r) and a point A in its plane :

1. If  =  r, the point B lies on the circle.
2. If   < r, the point A lies in the interior of  the circle         (i.e., inside the circle).
3. If   > r, the point C lies in the exterior of the circle          (i.e., outside the circle).

Separation of the plane of a circle by the circle  :  A circle separates the plane of the circle in three disjoint sets : (1) The circle,  (2) The interior of the circle,  (3) The exterior of the circle.

Chord and Secant  :  A line-segment whose end-point lie on a circle is known as a chord of the circle and the line containing a chord of the circle is called a secant of the circle.

In the figure,  is a chord of  ⊙ (P, r) while AB is a secant of the circle.

Radius :  A line-segment, whose one end-point is the center of a circle and the other end-point is a circle is called a radius of the circle

Chord  and  Secant  :  A line-segment whose end-point lie on a circle is known as a chord of the circle and the line containing a chord of the circle is called a secant of the circle.

In the figure,  is a chord of  ⊙ (P, r) while is a secant of the circle. is a secant of the circle.

• Diameter : A chord passing through the centre of a circle is called diameter of the circle.

In the given figure,  is a diameter of the circle with centre P.

The length of a diameter is denoted by d.

Here,  d  =  2r

The following facts are clear from the definition of a circle.

1. A circle is a plane figure.
2. The centre of a circle is in the plane of the circle but it is not a point of the   circle.

●  Congruent circles : Circles with different centres and equal radii are called congruent circles.

● Concentric circles  :  Circles, lying in the same plane and having the same centre but having radii of different measures, are called concentric circles.

The set of all the points of the plane of a circle, each of which is at a distance greater than the radius of the circle, from the centre of the circle, is called the exterior of the circle.

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