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DEFINATION OF CIRCLE.

DEFINATION 1:.

If a point moves such that its distance from the fixed point C is always a constant r () then the locus of that point is called a circle.

1.Here the fixed point is the centre of the circle.

2.The constant distance r is the radius of the circle

Defination 2:.

The locus of a point 'P'such that the ratio of itsdistance from two points A and B is constant K() is acircle.(If k= then the locus is a straight line)

Diameter: The locus of midpoints system of parallel chords of a curve is called as a diameter of that curve

Some important aspects of a circle :.

1.Angle in a semi circle is right angle (i.e ).

2.The angle made by a chord of a circle at the center of the circle is double to the angle made by the chord at any point of the circle.

3.Any three points on the circle are non-collinear.

4.Trough three non-collinear points only one circle passes through them.

5.The line joining mid points of a chord and center of the circle is perpendicular to the chord

6.Perpendicular bisectors of a chord of a circle passes through center of the circle.

7.If A and B are two points on the circle then

i).The line through A and B is called a secant line

ii).The line segment is called a chord of the circle and the length of the chord is denoted by AB.

8.Two tangents can be drawn from an external point on the circle.

9.Only one tangent can be drawn at a given point on the circle.

10.No real tangent can be drawn from internal point of a circle.

11.A line is tangent to a circle then the length of the perpendicular from center to that line is radius.

12.If a quadrilateral is inscribed in a circle,then the opposite angles are supplementary.

13.The chord of a circle with maximum length is diameter.

14.A diameter of a circle is a chord but a chord need not be a diameter.

15.Circles with same center are called as concentric circles.