# Circles and sectors

1. Nov 23, 2009

### look416

1. The problem statement, all variables and given/known data
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$$\theta$$)​

2. Relevant equations

3. 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
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 4, 2017
2. Nov 23, 2009

### rock.freak667

Re: Circle

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