#### 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.

#### Solution

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°

Is there an error in this question or solution?

Solution 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. Concept: Chord Properties - a Straight Line Drawn from the Center of a Circle to Bisect a Chord Which is Not a Diameter is at Right Angles to the Chord.