# Circles and sectors

## Homework Statement

The diagram shows a semicircle APB on AB as diameter. The midpoint of AB is O. The point P on the semicircle is such that the area of the sector POB is equal to twice the area of the shade segment. Given that angle POB is $$\theta$$ radians, show that

3$$\theta$$ = 2($$\pi$$-sin$$\theta$$)​

## The Attempt at a Solution

using formula
Area of circle = $$\frac{1}{2}$$r2$$\theta$$
and
Area of segment = $$\frac{1}{2}$$r2 ($$\theta$$ - sin $$\theta$$ )
heres the problems
from the picture http://img130.imageshack.us/img130/1790/001tz.jpg [Broken]
questions 4
the the angle of the segment is $$\pi$$-$$\theta$$
there im clueless even i inserted the info i have
what i really get is
$$\theta$$=2[$$\pi$$-$$\theta$$-sin($$\pi$$-$$\theta$$)]​
of course we cant use formula blindly so anyone can help me there

## The Attempt at a Solution

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## Answers and Replies

rock.freak667
Homework Helper

If sector POA contains the shaded segment and triangle POA, how do you find the area of the shaded region?