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Definition of circle 6

One point and two points 7

Chord of a circle 8

Perpendicular bisector of a line 9

Principles relating to chord and perpendicular bisector 10

Figures relating to principles 11

Uses and application 12

Length of chords - facts 14

Formula for length of chord 15

Three points 16

Circumcentre and circumcircle 17

Method of drawing a circumcircle 18

Generalisation of circumcircles 19

CIRCLE - DEFINITION

The path of a point which is at a fixed distance from a fixed point in the plane is called a circle

The fixed point is called the centreThe fixed distance is called the radius.

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ONE POINT TWO POINTS

Many circles can be drawn which Many circles of different radii can be drawnpasses through a point which pass through two points

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CHORD OF A CIRCLE

The line joining any two points on the circle is called a CHORD.

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A

AB is the chord of the circle.

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PERPENDICULAR BISECTOR OF A LINE

The locus of a point which moves at a fixed distance from the points A and B is the perpendicular bisector of AB.

A B

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Figures relating to the principles

Relating to the mid point of the chord , the Relating to the centre and the perpendicularperpendicular bisector and centre bisectors of the chord

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3. The bisector of the angle formed by extending two non parallel and equalchords, passes through the centre of the circle

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FORMULA FOR LENGTH OF CHORD

If the length of the chord l, radius of circle r, distance from the centre to the chord d, then

l = 2 𝒓𝟐 − 𝒅𝟐

Or

d

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THREE POINTS

If three points are on a straight line, we cannot draw a circle passing through these three points

If three points are not on a straight line, we can draw a circle passing through these points by taking the point of intersection of the perpendicular bisectors of the line joining the three points

CIRCUMCIRCLE AND CIRCUMCENTRE

The centre which passes through the three vertices of a triangle is called the circumcircle.

The centre of the circumcircle is called circumcentre.

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