# help on circles

• Dec 16th 2008, 04:14 AM
helloying
help on circles
help me solve part (b)
• Dec 16th 2008, 06:13 AM
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.

• Dec 17th 2008, 05:34 PM
helloying
Quote:

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.

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.