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    Question

    A chord, at a distance of 1 unit from the centre, has a

    length equal to k² sin  (π/4) and the radius of the circle is (-k) sin(π/3). What is the value of k, if k is an integer?
    A 4 Correct Answer Incorrect Answer
    B 2 Correct Answer Incorrect Answer
    C –2 Correct Answer Incorrect Answer
    D 3 Correct Answer Incorrect Answer

    Solution

    Radius = (-k) sin(π/3) = -√3k/2 Distance from chord to centre = OM = 1unit MR = length of chord/2 = [k2sin(π/3)]/2 = k2/2√2 In triangle OMR, => OM2 + MR2 = OR2 ⇒ 1 + k4/8 = 3k2/4 ⇒ k4 - 6k2 + 8 = 0 By hit and trial method, we get k = -2

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