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    Question

    AB and CD are parallel tangents to a circle with center

    O. Points P and Q are on AB and CD, respectively, such that PQ touches the circle at R. Find the measure of ∠ POQ.
    A 85º Correct Answer Incorrect Answer
    B 90° Correct Answer Incorrect Answer
    C 80º Correct Answer Incorrect Answer
    D 100° Correct Answer Incorrect Answer

    Solution

    Since PQ is tangent to the circle at R, PO bisects the angles at Thus, EOP = POR = θ 1 (let) QO bisects the angle at FOR. Thus, FOQ = QOR = θ ₂ (let) Since AB and CD are parallel tangents to the circle, EF must be a straight line. Thus, from the diagram, 2 (θ 1 + θ 2) = 180° (θ 1 + θ 2) = 90° POQ = 90°

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