UPSC CDS 1 2018 Math Paper

As radius is perpendicular to the tangent.
∴ ∠OPQ = 90° – α
also,
∠OPQ =∠OQP
= 90°– α(radii are equal)
Now,in ΔOPQ,
∠O +∠P + ∠Q =180°(Angle sum property)
⇒ ∠POQ + 90° – α + 90° – α
=180°⇒∠POQ = 2α