# Circular measure

1. Sep 28, 2009

### look416

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. Sep 28, 2009

### Mentallic

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