1.22: Figure 1 shows a circle, centre , with radius cm.

4PM1/2/June/2023 — Question 3 · 6 marks

1.22 diagram 1
Figure 1 shows a circle, centre O\displaystyle O, with radius r\displaystyle r cm.
The points A\displaystyle A, P\displaystyle P and B\displaystyle B lie on the circle.
The obtuse angle AOB=θ\displaystyle AOB = \theta radians.
The area of the sector APBO\displaystyle APBO, shown shaded, is 372.4cm2\displaystyle 372.4 \mathrm{cm}^2 and the length of the arc APB\displaystyle APB is 53.2cm\displaystyle 53.2 \mathrm{cm}.
Find, to 3 significant figures where appropriate, the value of
(i) r\displaystyle r
(ii) θ\displaystyle \theta
(6)