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Thread: circle proof

  1. #1
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    circle proof

    circle proof-win_20170313_12_36_15_pro.jpg


    trying to use angles on the same arc theorem
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  2. #2
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    Re: circle proof

    Quote Originally Posted by markosheehan View Post
    Click image for larger version. 

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    trying to use angles on the same arc theorem
    $ \begin{align*}|\angle CDL|&=0.5(|arc(CL)|-|arc(AB)|\\|\angle CAL|&=0.5|arc CL|\\|\angle ACB|&=0.5|arc AB| \end{align*}$
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  3. #3
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    Re: circle proof

    im confused. how does the angle CDL =.5 the size of the arc CL - size of arc AB
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  4. #4
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    Re: circle proof

    Quote Originally Posted by markosheehan View Post
    im confused. how does the angle CDL =.5 the size of the arc CL - size of arc AB
    $|\angle CDL|=0.5(|arc(CL)|-|arc(AB)|)$
    The point $D$ is exterior to the circle. The segments $\overline{DC}~\&~\overline{DL}$ both intersect the circle "cutting off" two arcs.
    It is a theorem that $|\angle CDL|$ is one-half the difference in the measures of the major & minor arcs.
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