Question

in fig , pq and pr are tangents draw from p if < qsr =40°, then <qpr is​

Answer 1

Answer:

In quadrilateral PQOR,  ∠P+∠PQO+∠PRO+∠QOR=360∘

But ∠PQO=∠PRO=90∘    (Tangent is perpendicular to radius at point of contact)

Thus, 50∘+90∘+90∘+∠QOR=360∘

So, ∠QOR=130∘

In triangle OQR, ∠OQR+∠ORQ+∠QOR=180∘

Hence, 2.∠OQR+∠QOR=180∘    

(because, ∠OQR=∠ORQ; (since OQ=OR, radii ))

Thus, 2.∠OQR+130∘=∠180∘

So, ∠OQR=25∘

Therefore option A is the answer