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The figure shows two circles centres C and D of radii 8 cm and 10 cm respectively. The two circles subtend angles θ and β respectively at their centres and intersect at A and B as shown.
a) Given that the area of triangle #ACB = 30.07 cm^2# and that of triangle #ADB = 43.30 cm^2#, calculate the size of the
i. angle marked θ.
ii. angle marked β.
b) Calculate to 2 decimal places the area of
i. sectors ACB and ADB
ii. the shaded region