In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

Asked by Pragya Singh | 2 years ago |  110

1 Answer

Solution :-

The dimensions of the circle are

Diameter = 40 cm

Radius = \( \dfrac{40}{2}\) = 20 cm

Consider AB be as the chord of the circle i.e. length = 20 cm

In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the  length of minor arc of the chord.

In ΔOAB,

Radius of circle = OA = OB = 20 cm

Similarly AB = 20 cm

Hence, ΔOAB is an equilateral triangle.

θ = 60° = \( \dfrac{\pi}{3}\) radian

We know that, 

in a circle of radius r unit, if an angle θ radian at the centre is subtended by an arc of length l unit then

We get θ = \( \dfrac{1}{r}\)

\( \dfrac{\pi}{3}=\dfrac{arc \;AB}{20}\)

arc AB= \( \dfrac{20\pi}{3}\)cm

Therefore, the length of the minor arc of the chord is \( \dfrac{20\pi}{3}\) cm.

Answered by Abhisek | 2 years ago

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