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Construct all the dotted red lines as shown. We are trying to find ∠ C A B = ∠ C A O .
Consider the cyclic quadrilateral A D C F . As opposite angles in a cyclic quadrilateral equal 1 8 0 ° , ∠ A F C = 6 0 ° .
As angles at the centre are equal to twice the angles at the circumference, ∠ A O C = 2 ∠ A F C = 1 2 0 ° .
As A O and C O are radii, △ A O C is isosceles, and hence the base angles are both equal to x .
⇒ 1 2 0 ° + 2 x = 1 8 0 ° ⇒ x = 3 0 °
Hence the statement is True .