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Math Help - Circle Geometry: Determine Size of Angle in Terms of Unknown

  1. #1
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    Circle Geometry: Determine Size of Angle in Terms of Unknown

    A chord BC and the diameter from A meet at a point P such that OC = CP. If angle CPO = a, prove that angle AOB = 3a. This is a method of trisection an angle by construction.

    What does this trisection of angle mean? Are there any other methods of solution?
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    MHF Contributor red_dog's Avatar
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    Let D be the other point of intersection between AP and the circle.

    We have m(\widehat{AOB})=m(arcAB)=x

    Then:

    a=m(\widehat{BPA})=\displaystyle\frac{m(arcAB)-m(arcCD)}{2}=\displaystyle\frac{x-a}{2}

    a=\displaystyle\frac{x-a}{2}\Rightarrow 2a=x-a\Rightarrow x=3a
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  3. #3
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    Sorry, i am just not seeing it. Mabey its the notations, that i am not use to.

    Can you just tell me what arcCD represents? Is it subtended at centre or circumference.
    And i can guess that m is the angle size?

    And also, the 2nd line, containing m(arc AB) - m(arc CD), what rule is that? Just point me in the right direction?
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