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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 72тБ░ Correct Answer Incorrect Answer
    C 59тБ░ Correct Answer Incorrect Answer
    D 49тБ░ Correct Answer Incorrect Answer

    Solution

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

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