AP and AQ are two tangents drawn to a circle with center O from an external point A. If ∠PAQ = 40°, then ∠POQ is:
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 140°.
∠PAQ = 40°
The tangent of a circle is perpendicular to the radius.
The sum of the four angles of a quadrilateral is 360°.
Here, PAQO is a quadrilateral.
So, ∠PAQ + ∠OPA + ∠OQA + ∠POQ = 360°
⇒ 40° + 90° + 90° + ∠POQ = 360°
⇒ ∠POQ = 360° - 220° = 140°
Therefore, the value of ∠POQ is 140°.