The diagram shows a circle, centre 0, with radius 4 cm. Points A and B lie on the circumference of the circle and AOB = 0, where o ses.
diagram not to scale
B
la. Find the area of the shaded region, in terms of O.
[3 marks]
1b. The area of the shaded region is 12 cm. Find the value of e.
[3 marks]

a = 49°

Step-by-step explanation:

OB = OC ( both radii of the circle ), thus

Δ BOC is isosceles and the base angles are congruent, that is

∠ OBC = ∠ OCB = 41° , so

∠ BOC = 180° - (2 × 41)° = 180° - 82° = 98°

The angle on the circumference BAC is half the angle at the centre for angles subtended on the same arc , thus

a = 0.5 × 98° = 49°