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Circular measure

  1. Sep 28, 2009 #1
    1. The problem statement, all variables and given/known data
    A chord of a circle subtends an angle of θ radians at the centre of the circle. The area of the minor segment cut off by the chord is one eighth of the area of the circle. Prove that 4θ = π + 4 sin θ


    2. Relevant equations
    s = rθ
    area of sector = 1/2 r2θ
    area of minor segment = area of sector - area of triangle
    = 1/2 r2θ - 1/2 ab sin θ

    3. The attempt at a solution
    1/2r22π x 1/8 = area of minor segment
    area of minor segment = 1/2r2θ - 1/2 ab sin θ
    1/2r22π x 1/8 = 1/2r2θ - 1/2 ab sin θ
    well the problem is i dont know what is the value of ab
     
  2. jcsd
  3. Sep 28, 2009 #2

    Mentallic

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    Homework Helper

    the area of the triangle is [tex]\frac{1}{2}absinC[/tex] right?
    The a and b are the sides of the triangle adjacent to the angle. They're the radii of the circle.
     
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