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Question
If AB, BC and CD are equal chords of a circle with O as centre and AD diameter, than ∠AOB =
Options
60°
90°
120°
none of these
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Solution
60°
As we know that equal chords make equal angle at the centre.
Therefore,
\[\angle AOB = \angle BOC = \angle COD\]
\[\angle AOB + \angle BOC + \angle COD = 180° \left[ \text{ Linear pair } \right]\]
\[ \Rightarrow 3\angle AOB = 180°\]
\[ \Rightarrow \angle AOB = 60° \]
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