Question

In the given figure, AB is the chord to the circle centred at O. If AC = CB and $\angle AOC={60}^{\circ }$, then find $\angle CAO$.

Answer 1

In the given figure, AB is the chord and AC = CB.
Since OC is bisecting the chord AB, OC will be perpendicular to AB.
(The line drawn through the center of a circle to bisect a chord is perpendicular to the chord)

Hence, $\angle OCA={90}^{\circ }$

Now in $\Delta OAC$,
$\angle OCA={90}^{\circ }$
$\angle AOC={60}^{\circ }$
So, $\angle CAO={180}^{\circ }-({60}^{\circ }+{90}^{\circ })={30}^{\circ }$