In the given figure, O is the centre of the circle, PQ is a chord and PT is the tangent at P.

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).