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Math Help - Another Radions/Arcs/Circles problem

  1. #1
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    Another Radions/Arcs/Circles problem

    A chord of a circle subtends an angle of theta radians at the centre of the circle. The area of the minor segment cut off by the chord is 1/8 of the area of the circle.

    Prove that 4theta= pi + 4 sin theta

    Ahhh i have no idea how to do it?
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  2. #2
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    Hello juliak
    Quote Originally Posted by juliak View Post
    A chord of a circle subtends an angle of theta radians at the centre of the circle. The area of the minor segment cut off by the chord is 1/8 of the area of the circle.

    Prove that 4theta= pi + 4 sin theta

    Ahhh i have no idea how to do it?
    If the radius of the circle is r, the area of the sector that makes an angle \theta at the centre is \tfrac12r^2\theta. The area of the triangle with two sides of length r enclosing an angle of \theta is \tfrac12r^2\sin\theta.

    So the area of the segment = ... - ... = \tfrac18\pi r^2

    Fill in the gaps; multiply both sides by 8, divide by r and you're there.

    Grandad
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