Triangle ABC has AB = 9 cm, BC = 10 cm and CA = 5 cm. A circle, center A and radius 3 cm, intersects AB and AC at P and Q respectively, as shown in the diagram.

a. Show that, to 3 decimal places, ∠BAC = 1.504 radians.

b. Calculate:

i. The area, in cm², of the sector APQ

ii. The area, in cm², of the shaded region BPQC

iii. The perimeter, in cm, of the shaded region BPQC.

5cm /Q P -10 cm- 9 cm B