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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 тИа EOP.
    A 80┬║ Correct Answer Incorrect Answer
    B 90┬░ Correct Answer Incorrect Answer
    C 85┬░ 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 тИа EOR. Thus, EOP = POR = ╬╕ 1 (let) QO bisects the angle at FOR. Thus, FOQ = QOR = ╬╕ тВВ (let) Since AB and CD are parallel tangents to the circle, EF must be a straight line. Thus, from the diagram, тИа EOP + POR + FOQ + QOR = 180┬░ 2 ( ╬╕ 1 + ╬╕ 2 ) = 180┬░ ( ╬╕ 1 + ╬╕ 2 ) = 90┬░ тИа EOP = 90┬░

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