Basic Definitions and Concepts on the Circle Explanation

 Basic Definitions and Concepts on the Circle



The circle:

It is the set of points of the plane which are at a constant distance from a fixed point in the same plane.


- The fixed point is called “the centre of the circle”.

- The constant distance is called “the radius length of the

   circle”.

- The circle is usually denoted by its centre, the circle M means the circle whose centre is the point M.


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Partition of the plane by the circle:


The surface of the circle :

It is the set of points of the circle  the set of points inside it.



The radius of the circle

It is a line segment whose endpoints are the centre of the circle and any point on the circle.


Notice that:

1- Any circle has an infinite number of radii and all of them are equal in length.

2- If two radii of two circles are equal in length, then the two circles are congruent and

      vice versa.

The chord of the circle:

It is a line segment whose endpoints are any two points on the circle.


The diameter of the circle:

It is a chord passing through the centre of the circle.


Notice that:

1- Any circle has an infinite number of diameters and all of them are equal in length.

2- The diameter of the circle is the longest chord of the circle, and its length = 2r


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Example (1)

Important corollaries

Corollary (1)

The straight line passing through the centre of the circle and the midpoint of any chord of it is perpendicular to this chord.

 

Corollary (2)

The straight line passing through the centre of the circle perpendicular to any chord of it bisects this chord.

Corollary (3)

The perpendicular bisector to any chord of a circle passes through the centre of the circle.


Example (2)


Example (3)

Example (4)












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