In the given figure, O is the centre of the circle, PQ is a chord and PT is the tangent at P.
Question:
In the given figure, O is the centre of the circle, PQ is a chord and PT is the tangent at P. If ∠POQ = 70∘ , then ∠TPQ is equal to
(a) 35∘
(b) 45∘
(c) 55∘
(d) 70∘
Solution:
We know that the radius and tangent are perperpendular at their point of contact
Since, OP = OQ
∵POQ is a isosceles right triangle
Now, In isoceles right triangle POQ
∠POQ + ∠OPQ + ∠OQP = 180∘ [Angle sum property of a triangle]
⇒ 70∘ + 2∠OPQ = 180∘
⇒ ∠OPQ = 55∘
Now, ∠TPQ + ∠OPQ = 90∘
⇒ ∠TPQ = 35∘
Hence, the correct answer is option (a).