In a circle of diameter 40cm the lenght of the chord 20cm find the lenght of minor arc of the chord?
Answers
then rad. = 20 cm
now chord = 20cm
the triangle formed is an equilateral triangle with each side = 20cm
Θ = 60°
now length of the arc is I = rΘ
= 20(60°*п(pi) /180°)
= 20π/3cm
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Given : a circle of diameter 40cm,the length of a chord is 20 cm,
To Find : the length of the minor arc of the chord
Solution:
Chord Length = 20 cm
Diameter = 40 cm
Perpendicular from center on chord bisect the chord
Hence Half of chord = 10 cm
Radius = 40/2 = 20 cm
Sin ( 1/2 of chord angle ) = 10 /20
=> 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 = 20 cm
Chord length = 20 cm
Hence it forms an Equilateral triangle
Hence angle formed by chord at center = 60°
Minor arc angle = 60°
length of the major arc of the chord = (60/360) * 2π * Radius
= ( 1/6 ) * 2π * 10
= 10π/3
= 50 * 3.14/3
= 10.47 cm
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