Question

In the given figure, PQ and PR are tangents to a circle centred at O. If ∠QPR = 35° then ∠QOR is equal to ________.

पर्याय

• 70°

• 90°

• 135°

• 145°

Answer 1

In the given figure, PQ and PR are tangents to a circle centred at O. If ∠QPR = 35° then ∠QOR is equal to 145°.

Explanation:

Given, ∠QPR = 35°

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 ⊥ PR

⇒ ∠OQP = ∠ORP = 90°

So, in quadrilateral PQOR, we have

∠OQP + ∠ORP + ∠QPR + ∠QOR = 360°

215° + ∠QOR = 360°

∠QOR = 360° − 215°

= 145°