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The probability that the length of a randomly selected chord of a circle lies between 2/3 and 5/6 of its diameter is

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The probability that the length of a randomly selected chord of a circle lies between  2/3  and  5/6  of its diameter is

(a)  5/16

(b)  1/16

(c)  1/4

(d)  2/3

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1 Answer

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Best answer

Correct option   (c)  1/4

Explanation:

length of chord is 2asinθ

∴ 2/3(2a) < 2asinθ < 5/6(2a)

⇒  2/3 < sinθ < 5/6

⇒  √11/6 < cosθ <  √5/3

⇒  √11/6a < r <  √5/3a

∴ required probability is

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