In the diagram, the vertices of \(\Delta ABC\) lie on the circle with centre \(O\). The point \(D\) lies on \(BC\) such that \(\Delta ABD\) is isosceles and \(\angle ABC = x\).
Explain why \(\angle AOC =2x\). (2 marks)
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\(\text{Angles at circumference and centre are both on arc}\ AC\)
\(\therefore \angle AOC = 2x\)