Question

AOD is a diameter of the circle with centre O. Given that ∠BDA = 18° and ∠BDC = 38°.∠BCD equals

(a) 90°

(b) 108°

(c) 76°

(b) 52°

Answer 1

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^∘