Correct option is (b) 28°
In △AOB,
OA = OB (Radius of the circle)
Hence, ∠OBA = ∠OAB = x (Isosceles triangle property)
Also, ∠OBC = 90∘ (Angle between the radius an the tangent)
Now,
In △AOC,
∠ACB + ∠BAC + ∠ABC = 180∘
34∘ + x + x + 90∘ = 180∘
124∘ + 2x = 180∘
x = 28∘
Thus, ∠ABO = 28∘