In a circle of diameter 40 cm the length of a chord is 20 cm find length of minor arc of chord
r = triangle leg = 20
so is the base 20 so equilateral
so 60/360 = 1/6 of circle
(1/6)2 pi r
=(1/3)pi 20
= 20.94 cm
To find the length of the minor arc of a chord in a circle, we can use the formula:
Length of Arc = (Angle/360) * 2 * π * r
In this case, we are given the diameter of the circle, which is 40 cm. The length of the chord is 20 cm.
To find the angle formed by the chord in the center of the circle, we can use the relationship between the angle, the length of the chord, and the radius:
Angle = 2 * arcsin(chord/2r)
where r is the radius of the circle. In this case, r = 20 cm (half of the diameter).
Angle = 2 * arcsin(20/40)
= 2 * arcsin(0.5)
≈ 2 * 30°
= 60°
Now we can substitute this angle and the radius into the formula to find the length of the minor arc:
Length of Arc = (60/360) * 2 * π * 20
= (1/6) * 2 * π * 20
= (1/3) * π * 20
≈ 20 * π / 3
≈ 20 * 3.14 / 3
≈ 20.93 cm
Therefore, the length of the minor arc of the chord is approximately 20.93 cm.