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    Question

    A tangent is drawn from an external point P to a circle,

    touching the circle at point Q such that PQ = 16cm. A secant PRS is also drawn from P, intersecting the circle at points R and S. Given that PR = 8 cm, determine the length of the chord RS.
    A 24 cm Correct Answer Incorrect Answer
    B 12 cm Correct Answer Incorrect Answer
    C 16 cm Correct Answer Incorrect Answer
    D 18 cm Correct Answer Incorrect Answer

    Solution

    Image

    We know that,

    PQ 2  = PR × PS (Tangent secant theorem)

    So, 16 2  = 8 × PS

    Or, 256 = 8 × PS

    Or, PS = 32 cm

    RS = PS – PR

    So, RS = 32 – 8 = 24 cm
    Therefore, the length of chord is 24 cm.

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