Question

In the given figure, AB and AD are the tangents to the circle from an external point A. If ∠BCD = 40°, find ∠BAD.

Answer 1

For two tangents drawn from an external point A:

∠BAD + ∠BOD = 180∘

This is a standard theorem: angle between tangents + angle at centre = 180°.

∠BCD = 40°

This is an angle at the circle subtended by arc BD.

The angle subtended by the same arc at the centre:

∠BOD = 2 × ∠BCD = 2 × 40° = 80°

∠BAD + 80° = 180°

∠BAD = 180° − 80° = 100°