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If radius of a circle intersects a chord then it bisects the chord only if radius is perpendicular to the chord.
The radius of the circle that is perpendicular to a chord intersects the chord at its midpoint, so it is said to bisect the chord.
The relationship between the chord and the radius of the circle is Length of the chord = 2r sin(c/2) where r = radius of the circle and c = angle subtended at the center by the chord
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Radius