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ST is the diameter of a circle with centre O. Two tangents AB and CD are drawn at to the circle which touches the circle at point S and T respectively. If one more tangent EF is drawn to the circle which cuts tangents AB and CD at point P & Q respectively, then find the value of ∠POQ.

ST is the diameter of a circle with centre O. Two tangents AB and CD are drawn at to the circle which touches the circle at point S and T respectively. If one more tangent EF is drawn to the circle which cuts tangents AB and CD at point P & Q respectively, then find the value of ∠POQ. Correct Answer 90°

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In the figure∶

ΔPSO and ΔPRO are congruent and

ΔQTO and ΔQRO are congruent

∴ ∠SOP = ∠POR and

∠TOQ = ∠QOR

Since ∠SOT = 180°

∴ POQ = 180/2 = 90°

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