The correct option is
C We know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
∴ ∠OPR=90∘ ⇒ ∠OPQ+∠QPR=90∘ [From figure]
⇒ ∠OPQ=90∘−50∘=40∘ [∵∠QPR=50∘] Now, OP = OQ = Radius of circle
∴ ∠OQP=∠OPQ=40∘ [Since, angles opposite to equal sides are equal]
In
△OPQ,∠O+∠P+∠Q=180∘ [Since, angles opposite to equal sides are equal]
⇒ ∠O=180∘−(40∘−40∘) [∵∠P=40∘=∠Q] =
180∘−80∘=100∘