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.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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