eresourcebook padmaja
DESCRIPTION
Practicum on E resource bookTRANSCRIPT
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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
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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.
B
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
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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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