Question

In the given figure, O is the centre of the circle. AB is the tangent to the circle at the point P. If ∠APQ = 58^∘ then the measue of ∠PQB is [CBSE 2014]
(a) 32^∘
(b) 58^∘
(c) 122^∘
(d) 132^∘

Answer 1

We know that a chord passing through the centre is the diameter of the circle.
∵∠QPR = 90^∘ (Angle in a semi circle is 90^∘)
By using alternate segment theorem
We have ∠APQ = ∠PRQ = 58^∘
Now, In △PQR
∠PQR + ∠PRQ + ∠QPR = 180⁰ [Angle sum property of a triangle]
⇒ ∠PQR + 58^∘ + 90⁰ = 180^∘
⇒ ∠PQR= 32^∘
Hence, the correct answer is option (a).