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    Question

    Length of a chord in a circle of radius 'r' cm, is 40 cm

    and distance between chord and centre of the circle is 21 cm. Find the value of (2r + 1).
    A 55 Correct Answer Incorrect Answer
    B 59 Correct Answer Incorrect Answer
    C 61 Correct Answer Incorrect Answer
    D 63 Correct Answer Incorrect Answer

    Solution

    Image
    AB is the chord of circle.
    Perpendicular line joining the centre of circle and chord, bisects the chord.
    i.e. AC = BC = (40/2) = 20 cm
    By Pythagoras theorem,
    OA 2 = OC 2 + AC 2
    Or, r 2 = 21 2 + 20 2
    Or, r 2 = 441 + 400
    Or, r 2 = 841
    So, 'r' = 29
    But length cannot be negative. So, 'r' = 29
    Required value = 2 X 29 + 1 = 59

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