In Fig.1, PQ and PR are two tangents to a circle with centre O. If ∠QPR = 46°, then calculate ∠QOR

Question

Philoid · Accepted Answer

Given, PQ and PR are two tangents to a circle with centre O and ∠QPR = 46°.

Since, the radius drawn to these tangents will be perpendicular to the tangents,

OQ ⊥ PQ and OR ⊥ PR.

∴ ∠OQP = ∠ORP = 90°

We know that the sum of angles in a quadrilateral is 360°.

⇒ ∠OQP + ∠QPR + ∠ORP + ∠QOR = 360°

⇒ 90° + 46° + 90° + ∠QOR = 360°

⇒ 226° + ∠QOR = 360°

⇒ ∠QOR = 360° - 226°

∴ ∠QOR = 134°

Ans. ∠QOR = 134°