3.10: Circle with chord and consecutive arcs

0606/13/M/J/22 — Question 2 · 7 marks

3.10 diagram
In this question, all lengths are in centimetres and all angles are in radians.
The diagram shows a circle, centre OO, radius 88. The points AA, BB and CC lie on the circumference of the circle. The chord ABAB has length 1010.
(a)
Show that angle BOABOA is 1.351.35 correct to 22 decimal places.
[2]
(b)
Given that the minor arc BCBC has a length of 1818, find angle BOCBOC.
[2]
(c)
Find the area of the minor sector AOCAOC.
[3]