PQ is the diameter of a circle with centre O. PT is a tangent touching the circle at P. The secant QT intersects the circle at S. O and S are joined. If ∠ SOP = 104°, what is the measure (in degrees) of ∠PTQ?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 38.
∠OQS = ∠OSQ [OS = OQ (radius)]
But,
∠SOP = ∠OQS + ∠OSQ [By exterior angle theorem]
⇒ 104° = 2 ∠OQS
Now, In △QPT
⇒ ∠PTQ + ∠OQS + ∠QPT = 180°
⇒ ∠PTQ = 180 - ∠OQS - ∠QPT
⇒ ∠PTQ = 180° - 52° - 90°
⇒ ∠PTQ = 38°