1.19: Composite figure with an arc and a triangle

0606/13/O/N/20 — Question 8 · 8 marks

In this question all lengths are in centimetres.

1.19 diagram
The diagram shows the figure ABCABC. The arc ABAB is part of a circle, centre OO, radius rr, and is of length 1.45r1.45r. The point OO lies on the straight line CBCB such that CO=0.5rCO = 0.5r.
(a)
Find, in radians, the angle AOBAOB.
[1]
(b)
Find the area of ABCABC, giving your answer in the form kr2kr^{2}, where kk is a constant.
[3]
(c)
Given that the perimeter of ABCABC is 12 cm12\text{ cm}, find the value of rr.
[4]