1.5: Intersecting circles and lens-shaped region

The diagram shows a circle, centre , radius , intersecting a circle, centre , radius . The two circles intersect at the points and . The radii and are tangents to the circle with centre . The radii and are tangents to the circle with centre .
(i)[2]
Show that angle is radians, correct to significant figures.
(ii)[1]
Find angle in radians.
(iii)[3]
Find the perimeter of the shaded region.
(iv)[4]
Find the area of the shaded region.
