Question

If AB, BC and CD are equal chords of a circle with O as centre and AD diameter, than ∠AOB =

(a) 60°

(b) 90°

(c) 120°

(d) none of these

Answer 1

(a) 60°



As we know that equal chords make equal angle at the centre.

Therefore,

$$\begin{gathered} \angle AOB=\angle BOC=\angle COD \\ \angle AOB+\angle BOC+\angle COD=180°\left[\mathrm{Linear}\mathrm{pair}\right] \\ \Rightarrow 3\angle AOB=180° \\ \Rightarrow \angle AOB=60° \end{gathered}$$

Hence, the correct answer is option (a).