Question

5. If PQ and PR are two tangents to a circle
with centre O. If ZQPR = 46°, find ZQOR.
[CBSE 2014]
46°
DP​

Answer 1

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°