If PQ and PR are the two tangents to a circle with center O, and ∠QOR=150°, then ∠QPR is equal to:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 30°.
Given : ∠QOR = 150°
PQ and PR are tangents.
Therefore, the radius drawn to these tangents will be perpendicular to the tangents.
So, we have OQ ⊥ PQ and OR ⊥ RP.
⇒ ∠OQP = ∠ORP = 90°
So, in quadrilateral PQOR, we have
∠OQP + ∠QPR + ∠PRO + ∠ROQ = 360°
⇒ 90° + ∠QPR + 90° + 150° = 360°
⇒ ∠QPR = 360° − 330° = 30°