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    Question

    In a circle, two radii OA and OB form a central angle of

    120°. If the length of chord AB is 10 cm, what is the radius of the circle (in cm)?
    A 5 cm Correct Answer Incorrect Answer
    B 5√3 cm Correct Answer Incorrect Answer
    C 10/√3 cm Correct Answer Incorrect Answer
    D 10 cm Correct Answer Incorrect Answer

    Solution

    ATQ, For a circle of radius R and central angle θ, chord length c = 2R sin(θ/2). Here: c = 10, θ = 120° ⇒ θ/2 = 60°. 10 = 2R sin 60° = 2R × (√3/2) = R√3 ⇒ R = 10/√3 cm.

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