Circles and sectors

  • Thread starter look416
  • Start date
  • #1
87
0

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 [tex]\theta[/tex] radians, show that

3[tex]\theta[/tex] = 2([tex]\pi[/tex]-sin[tex]\theta[/tex])​


Homework Equations





The Attempt at a Solution


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

Homework Statement





Homework Equations





The Attempt at a Solution

 
Last edited by a moderator:

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31


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

Related Threads on Circles and sectors

  • Last Post
Replies
5
Views
6K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
5K
  • Last Post
Replies
9
Views
4K
Top