1.11: Crescent between an arc and a semicircle

0606/12/O/N/17 — Question 10 · 8 marks

1.11 diagram1.11 diagram
The diagram shows an isosceles triangle ABCABC, where AB=AC=5 cmAB = AC = 5\text{ cm}. The arc BECBEC is part of the circle centre AA and has length 6.2 cm6.2\text{ cm}. The point DD is the midpoint of the line BCBC. The arc BFCBFC is a semi-circle centre DD.
(i)
Show that angle BACBAC is 1.241.24 radians.
[1]
(ii)
Find the perimeter of the shaded region.
[3]
(iii)
Find the area of the shaded region.
[4]