**Question 7**:

Diagram below shows a circle with centre

*O*and radius 12 cm.Given that

*A*,

*B*and

*C*are points such that

*OA*=

*AB*and ∠

*OAC*= 90°, find

**(a)**∠

*BOC*, in radians,

**(b)**the area, in cm

^{2}, of the shaded region.

*Solution:***(a)**For triangle

*OAC,*

cos ∠

*A**OC*= 6/12 Ð

*A**OC*= 1.047 rad (change calculator to Rad mode)**Ð**

*B*

*OC*= 1.047 rad**(b)**

Area of the shaded region

= Area of

*BOC*– Area of triangle*AOC*= ½ (12)

^{2}(1.047) – ½ (6) (12) sin 1.047 (change calculator to Rad mode)= 75.38 – 31.17

=

**44.21 cm**^{2}**Question 8**:

Diagram below shows a sector

*QOR*of a circle with centre*O*.It is given that

*PS*= 8 cm and*QP*=*PO*=*OS*=*SR*= 5 cm.Find

**(a)**the length, in cm, of the arc

*QR*,

**(b)**the area, in cm

^{2}, of the shaded region.

*Solution:***(a)**Length of arc

*QR*=

*r*θ = 10 (1.75) =

**17.5 cm**

**(b)**

Area of the shaded region

= Area of sector

*QOR*– Area of triangle*POS*= ½ (10)

^{2}(1.75) – ½ (5) (5) sin 1.75 (change calculator to Rad mode)= 87.5 – 12.30

=

**75.2 cm**^{2}