Circle Geometry, SMB-008

In the diagram, \(AC\) is a diameter of the circle centred at \(O\), and \(OA = AB\).

Find the value of \(\theta\). (3 marks)

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\(\theta = 30^{\circ}\)

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\(\angle ABC=90^{\circ}\ \ \text{(angle in semi-circle)}\)

\(OA=OB\ \ \text{(radii)} \)

\( \angle OAB=60^{\circ}\ \ ( \Delta OAB\ \text{is equilateral}) \)

\(\theta\)	\(= 180-(90+60)\ \ (180^{\circ}\ \text{in}\ \Delta) \)
	\(= 30^{\circ} \)