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    Question

    In a circle of radius 5√13 cm, a chord is at a

    distance of 10 cm from the centre of the circle. Find the length (in cm) of the chord. 
    A 30 Correct Answer Incorrect Answer
    B 28 Correct Answer Incorrect Answer
    C 36 Correct Answer Incorrect Answer
    D 15 Correct Answer Incorrect Answer

    Solution

    In a circle, a perpendicular line from the center to a chord bisects the chord. So we form a right triangle: One leg = distance from center to chord = 10 cm Hypotenuse = radius = 5√13cm Half of the chord = unknown (let's call it x) Apply the Pythagorean Theorem:

    So, half the chord = 15 cm Therefore, full chord length = 2×15= 30 cm

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