The points \(A\), \(B\), \(C\), \(D\) and \(E\) lie on a circle with centre \(O\). The lines \(HI\) and \(BI\) are tangents to the circle at \(C\) and \(B\) respectively. \(BC\) intersects \(AE\) at \(G\). Given that angle \(ABC=76^\circ\), angle \(OAB=62^\circ\) and angle \(DAE=70^\circ\).
Show that triangle OBI is congruent to triangle OCI. Give a reason for each statement you make.[2]
Giving reasons for each step of your working, find
angle \(DCB\),[1]
angle \(GCO\),[2]
angle \(BCH\).[1]
In the figure, \(O\) is the centre of the circle and \(ABCO\) is a sector. Given that angle \(AOC=2.18\) radians, \(OA=OC=8\text{ cm}\) and \(CD=3.6\text{ cm}\).
Calculate the perimeter of ABCDA.[4]
Find \(\dfrac{\text{area of sector}\hspace{0.5em}ABCO}{\text{area of triangle}\hspace{0.5em}AOD}\). Give your answer correct to 2 decimal places.[3]
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