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    Question

    Length of a chord in a circle of radius 'r' cm, is 24 cm

    and distance between chord and centre of the circle is 35 cm. Find the value of (6r - 80).
    A 138 Correct Answer Incorrect Answer
    B 142 Correct Answer Incorrect Answer
    C 146 Correct Answer Incorrect Answer
    D 150 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 = (24/2) = 12 cm
    By Pythagoras theorem,
    OA 2 = OC 2 + AC 2
    Or, r 2 = 35 2 + 12 2
    Or, r 2 = 1225 + 144
    Or, r 2 = 1369
    So, 'r' = 37
    But length cannot be negative. So, 'r' = 37
    Required value = 6 X 37 - 80 = 142

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