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Question
Answer the following :
A wire of length 10 cm is bent so as to form an arc of a circle of radius 4 cm. What is the angle subtended at the centre in degree ?
Solution
Let θc be the angle subtended by the arc of length S = 10 cm at the centre of the circle.
Then S = rθ, where r = 4 cm
∴ 10 = 4θ
∴ θ = `10/4 = (5/2)^"c"`
Now, 1c = `(180/pi)^"c"`
∴ `(5/2)^"c" = (5/2 xx 180/pi)^circ`
= `(450/pi)^circ`
Hence, the angle subtended at the centre = `(450/pi)^circ`.
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