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Circles and sectors

  1. Nov 23, 2009 #1
    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 [tex]\theta[/tex] radians, show that

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


    2. Relevant equations



    3. 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
    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. jcsd
  3. Nov 23, 2009 #2

    rock.freak667

    User Avatar
    Homework Helper

    Re: Circle

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