Question:
PQ is a tangent to a circle with centre O at the point P. If △OPQ is an isosceles triangle, then ∠OQP is equal to
(a) 30∘
(b) 45∘
(c) 60∘
(d) 90∘
Solution:
We know that the radius and tangent are perperpendular at their point of contact
Now, In isoceles right triangle POQ
∠POQ + ∠OPQ + ∠OQP = 180∘ [Angle sum property of a triangle]
⇒ 2∠OQP + 90∘ = 180∘
⇒ ∠OQP = 45∘
Hence, the correct answer is option (b).