Question

In the figure, AB is the chord of a circle with centre O and DOC is a line segment such that BC = DO. If ∠C = 20°, find angle AOD.

Answer 1

Join OB,

In ΔOBC,

BC = OD = OB  ...(Radii of the same circle)

∴ ∠BOC = ∠BCO = 20°

And Ext. ∠ABO = ∠BCO + ∠BOC

`=>` Ext. ∠ABO = 20° + 20° = 40°  ...(i)

In ΔOAB,

OA = OB  ...(Radii of the same circle)

∴ ∠OAB = ∠OBA = 40°   ...(From (i))

∠AOB = 180° – ∠OAB – ∠OBA

`=>` ∠AOB = 180° – 40° – 40° = 100°

Since DOC is a straight line

∴ ∠AOD + ∠AOB + ∠BOC = 180°

`=>` ∠AOD + 100° + 20° = 180°

`=>` ∠AOD = 180° – 120°

`=>` ∠AOD = 60°