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P and Q are two points on a circle with centre at O. R is a point on the minor arc of the circle, between the points P and Q. The tangents to the circle at the points P and Q meet each other at the point S. If ∠PSQ = 20°, ∠PRQ =?   (SSC CGL 1st Sit. 2013)
  • a)
    100°
  • b)
    80°
  • c)
    200°
  • d)
    160°
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
P and Q are two points on a circle with centre at O. R is a point on t...

In quadrilateral POQS, ∠S = 20°
∠OPS = ∠OQS = 90°, ∠POQ = ?.
{Since PS and QS are tangent to the circle}
∴ Sum of angles in a quadrilateral = 360°
∠OPS + ∠S + ∠OQS + ∠POQ = 360°
90° + 20° + 90° + ∠POQ = 360°
⇒ ∠POQ = 160°

{Angle made on perimeter by the same chord is half of the angle made at the centre}

Now, In cyclic quadrilateral PRQT,
∠PTQ + ∠PRS = 180°
80° + ∠PRQ = 180°  ⇒ ∠PRQ = 180° – 80° = 100°
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P and Q are two points on a circle with centre at O. R is a point on the minor arc of the circle, between the points P and Q. The tangents to the circle at the points P and Q meet each other at the point S. If ∠PSQ = 20°, ∠PRQ =? (SSC CGL 1st Sit. 2013)a)100°b)80°c)200°d)160°Correct answer is option 'A'. Can you explain this answer?
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