Correct option is (b) 108°
Given, AD is diameter.
hence, ∠ABD = 90∘ (Angle is a semi circle)
Now, ∠ABC + ∠ADC = 180∘ (Opposite angles of cyclic quadrilateral)
90∘ + ∠DBC + 18∘ + 38∘ = 180∘
∠DBC = 34∘
Now, In △DBC
∠DBC + ∠BCD + ∠BDC = 180∘
34∘ + ∠BCD + 38∘ = 180∘
∠BCD = 108∘