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Math Help - Geometry Proof

  1. #1
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    Geometry Proof

    Geometry Proof-.jpg
    the circle has radius 1.
    OB=arcOA= \theta

    Prove that OP= 1-cos \theta

    Deduce that OD = \frac{\theta(1-cos\theta)}{\theta-sin\theta}

    thanks.
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  2. #2
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    is it known that the circle's center lies on the line OP? Is C the center of the circle? If yes, it's pretty obvious that CP = \cos\theta.

    For the second equality, let A' be the projection of A on OB. Use the fact that the triangle BA'A is similar to the triangle BOD.
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  3. #3
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    yes to your questions, but why cp=cos theta
    i cant see it, im stupid
    and can you explain the 2nd part in more details.

    thanks.
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  4. #4
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    Quote Originally Posted by BabyMilo View Post
    why cp=cos theta
    Because \angle OCA=\theta. The fact that CP=\cos\theta follows from the definition of cosine.

    and can you explain the 2nd part in more details.
    Draw a horizontal line through A and call its intersection with the line OB by A'. Then the triangle BA'A is similar to the triangle BOD because all three angles are equal. Therefore the ratio of A'A = OP to OD is the same as the raio of BA' to BO.
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