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Chord and Segment of A Circle
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Chord and Segment of A Circle
Chord :- a line segment Joining any 2 points on a circle is called a chord of the Circle.
Segment :- let PQ be a chord of the Circle C(O,r), then PQ divides the region enclosed by the circle into 2 parts .Each of the parts is called a segment of the Circle.
The segment containing the minor arc is called the minor segment, and the segment containing the major arc is called the major Segment.
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Example: In the Fig below, OS is perpendicular to the chord PQ of a circle whose centre is O. If QR is a diameter, show that RP = 2OS.
Solution: Since OD PQ and the perpendicular drawn from the centre to a chord bisects the chord.
S is the mid-point of PQ Also, O being the centre, is the mid-point of QR.
Thus, in PQR, S and O are mid-points of PQ and QR respectively.
Therefore, SO || PR And, SO = 1/2 PR
[Segment joining the mid-points of two sides j of a triangle is half of the third side] 
PR = 2SO
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