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    Question

    In a circle with centre O, PAX and PBY are the tangents

    to the circle at points A and B. from an external point P. Q is any point on the circle such that <QAX = 59° and <QBY = 72°. What is the measure of <AQB?
    A 31° Correct Answer Incorrect Answer
    B 72⁰ Correct Answer Incorrect Answer
    C 59⁰ Correct Answer Incorrect Answer
    D 49⁰ Correct Answer Incorrect Answer

    Solution

    Alternate segment theorem for ΔAQR, => <ARQ = <QAX Same for ΔQBR, => <BRQ = <QBR => <R = 59˚ + 72˚ = 131˚ Now, => <Q = 180˚ - <R => <Q = 180˚ - 131˚ => <Q = 49˚

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