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Thread: I need help with circle theorums

  1. #1
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    I need help with circle theorums

    Can i get help on this question. It is a 6 marker
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: I need help with circle theorums

    Actually, I'd start backward a bit. Angles ADO and ABO are both right angles. (Prove this!) Hence you can get angle DOB in terms of y.

    Can you fill in the steps?

    -Dan
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    Re: I need help with circle theorums

    it is really hard and I dont understand it
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    Forum Admin topsquark's Avatar
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    Re: I need help with circle theorums

    Another hint then: Knowing that angle ABO is a right angle, then you know that 2x + angle CBO + 90 degrees = 180 degrees. (Again, prove it.) So what is angle CBO in terms of x?

    Here's a site with a list of the circle theorems. Maybe having all of them in one spot might help.

    -Dan
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    Re: I need help with circle theorums

    Quote Originally Posted by Shook View Post
    it is really hard and I dont understand it
    Do you understand that $y=m(\angle BAD)=\frac{1}{2}\left( {arc(BCD) - arc(BD)} \right)~?$
    The quadrilateral $ABOD$ contains two right angles & the sum of all its angles is $2\pi$. Therefore $m(\angle BOD)=\pi-y.$
    Look at the figure: $m(\angle COD)=\pi-2x=m(arc DC)$; moreover since $2x=0.5(arc BC)$ then $4x=m(\angle COB)$.

    $m(\angle BOC)+m(\angle COD)+m(\angle DOB)=2\pi$ now you finish and sow us your work.
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