eresourcebook padmaja
Post on 13-Jun-2015
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WELCOME to mypracticum
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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.
6
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
7
CHORD OF A CIRCLE
The line joining any two points on the circle is called a CHORD.
B
A
AB is the chord of the circle.
8
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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