Math, asked by shravan200438, 8 months ago

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

Answered by amitnrw
1

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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