in a circle of diameter 20cm,the length of a chord is 10 cm, then the length of the major arc of the chord is
Answers
Given : a circle of diameter 20cm,the length of a chord is 10 cm,
To Find : the length of the major arc of the chord
Solution:
Chord Length = 10 cm
Diameter = 20 cm
Perpendicular from center on chord bisect the chord
Hence Half of chord = 5
Radius = 10 cm
Sin ( 1/2 of chord angle ) = 5 /10
=> Sin ( 1/2 of chord angle ) = 1/2
=> Sin ( 1/2 of chord angle ) = Sin 30°
=> 1/2 of chord angle = 30°
=> chord angle = 60°
Minor arc angle = 60°
or another way to get angle
as Radius = 10 cm
Chord length = 10 cm
Hence it forms an Equilateral triangle
Hence angle formed by chord at center = 60°
Major arc angles = 360° - 60° = 300°
length of the major arc of the chord = (300/360) * 2π * Radius
= ( 5/6 ) * 2π * 10
= 50π/3
= 50 * 3.14/3
= 52.33 cm
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