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Chord of a circle
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Chord of a Circle
A line segment joining any two points on a circle is called a chord of the circle. The diameter, passing through the circle's centre, is the longest chord in a circle.If two chords of a circle intersect, the intersection creates four line segments that have an interesting relationship.
It should be noted that a chord is not a part of the circle.
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Example: The radius of a circle is 12 cm and the length of one of its chords is 8 cm. Find the distance of the chord from the centre.
Solution: Let AB be a chord of circle with centre O and radius 12 cm such that AB= 8 cm.
From O, draw OLAB.
Join OA.
As perpendicular from the centre of a circle to a chord bisects the chord, therefore
AL = LB =1/2AB = 4 cm.
In right triangle OLA,
122 = OL2 + 42
122-42 = OL2
OL2 = 128
OL = 82 cm.
Hence, the distance of the chord from the centre is 82 cm.
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