1. ## help on circles

help me solve part (b)

2. ## Area

Hello -

Area of APBC = 2 x Area of triangle OBC + area of sector OAPB, found in part (a)

Area of triangle OBC = 0.5 x base x height, where base = OC and height = perpendicular distance from B to OP.

Height = OB x sin (angle BOP), and angle BOP = 2 x angle BCP (angle at centre = twice angle at circumference.

I hope you can do it now.

Hello -

Area of APBC = 2 x Area of triangle OBC + area of sector OAPB, found in part (a)

Area of triangle OBC = 0.5 x base x height, where base = OC and height = perpendicular distance from B to OP.

Height = OB x sin (angle BOP), and angle BOP = 2 x angle BCP (angle at centre = twice angle at circumference.

I hope you can do it now.

Thanks I got it now. However i got stuck in part (c) . Can u teach me please?

4. ## Area

Hi -

In triangle OBT we know OB = 6, angle BOT = $\frac{\pi}{3}$ and angle OBT = $90^o$. So you can work out the length of BT and hence the area of the triangle.

Then subtract the area of the sector OAPB (found in b) from area of quadrilateral OABT.