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 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.
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