1.5: Intersecting circles and lens-shaped region

0606/11/O/N/17 — Question 9 · 10 marks

1.5 diagram
The diagram shows a circle, centre AA, radius 10 cm10\text{ cm}, intersecting a circle, centre BB, radius 24 cm24\text{ cm}. The two circles intersect at the points PP and QQ. The radii APAP and AQAQ are tangents to the circle with centre BB. The radii BPBP and BQBQ are tangents to the circle with centre AA.
(i)
Show that angle PAQPAQ is 2.352.35 radians, correct to 33 significant figures.
[2]
(ii)
Find angle PBQPBQ in radians.
[1]
(iii)
Find the perimeter of the shaded region.
[3]
(iv)
Find the area of the shaded region.
[4]