True or False

Construct all the dotted red lines as shown. We are trying to find $\angle CAB = \angle CAO$ .

Consider the cyclic quadrilateral $ADCF$ . As opposite angles in a cyclic quadrilateral equal $180°$ , $\angle AFC = 60°$ .

As angles at the centre are equal to twice the angles at the circumference, $\angle AOC = 2 \angle AFC=120°$ .

As $AO$ and $CO$ are radii, $\triangle AOC$ is isosceles, and hence the base angles are both equal to $x$ .

$\Rightarrow~~ 120°+2x=180° ~~\Rightarrow~~ x= 30°$

Hence the statement is $\large\color{#20A900}{\boxed{\text{True}}}$ .