In the figure below, AB is a chord of a circle with centre O. A tangent AT is drawn at point A so that ∠BAT = 50°. Then ∠ADB = ?

Answer: Option B

Let take a point 'C' on circumference of circle
Then ∠BAT = ∠BCA = 50° (Alternate segment theorem)

In Cyclic Quadrilateral $$\square$$ ACBD
∠D = 180° - ∠C
(In a cyclic quadrilateral the sum of opposite angles is 180°)
Then ∠D = 180° - 50° = 130°