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    Question

    If radii of two concentric circles are 4 cm and 5 cm,

    then the length of eachchord of one circle which is tangent to the other circle is
    A 6 cm Correct Answer Incorrect Answer
    B 9 cm Correct Answer Incorrect Answer
    C 1 cm Correct Answer Incorrect Answer
    D 3 cm Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    We have two concentric circles with radii 4 cm and 5 cm. A chord of the larger circle is tangent to the smaller circle. We need to find its length. Identify Key Distances The radius of the larger circle = 5 cm The radius of the smaller circle = 4 cm (this is also the perpendicular distance from the center to the chord). The perpendicular from the center bisects the chord. Use Pythagoras Theorem In the right triangle formed: Hence Full Chord Length = AB=2×MB=2×3=6 cm

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