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Thread: circle proof

  1. #1
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    circle proof

    circle proof-win_20170129_13_11_53_pro.jpg

    i have worked out so far angle ADC and angle ASC=180 as its a cyclic quadrilateral. also 2*angle ADC= angle ABC so angle ABC= 180-180+angle ADC so ABC=ADC ABC=ADC
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    Re: circle proof

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

Name:	WIN_20170129_13_11_53_Pro.jpg 
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    i have worked out so far angle ADC and angle ASC=180 as its a cyclic quadrilateral. also 2*angle ADC= angle ABC so angle ABC= 180-180+angle ADC so ABC=ADC ABC=ADC
    2*angle ADC= angle ABC is not correct but rather
    2*angle ADC= angle AOC where O is the center of the circle through the points A,S,C,D
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  3. #3
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    Re: circle proof

    any other ideas on how to work it out . i still cant
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    Re: circle proof

    If OH is perpendicular to AS where H is on AS, then angle HOS + 90 degrees = angle OST

    OST is an exterior angle of triangle OHS
    Last edited by Idea; Jan 30th 2017 at 09:37 AM.
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  5. #5
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    Re: circle proof

    I think the trees are obscuring the forest. Look at this diagram:

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    Re: circle proof

    Quote Originally Posted by johng View Post
    I think the trees are obscuring the forest. Look at this diagram:

    indeed I see the forest now and it is beautiful.
    Thank you.
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    Re: circle proof

    how do you get ABC=180-.5ASC using angles on the same arc thorem i get 2ADC=ABC so ADC=.5ABC i know ADC+ASC=180 so .5ABC=180-ASC this differs to ABC=180-.5ASC
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    Re: circle proof

    Quote Originally Posted by markosheehan View Post
    how do you get ABC=180-.5ASC using angles on the same arc thorem i get 2ADC=ABC so ADC=.5ABC i know ADC+ASC=180 so .5ABC=180-ASC this differs to ABC=180-.5ASC
    $ \begin{align*}m(\text{arc}(ABC) &=m(\angle ASC)\\ &=\frac{1}{2}m(\text{arc}(ADC) \\&=\frac{1}{2}m(2\pi-\text{arc}(ASC)\\ &=m(\pi-\frac{1}{2}\text{arc}(ASC))\end{align*}$
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    Re: circle proof

    what does m stand for. i dont understand your notation how does m arcABC=mASC
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  10. #10
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    Re: circle proof

    $m \angle{ASC}$ is read "the measure of angle ASC"

    $\angle{ASC}$ is a central angle in the smaller circle. A central angle is equal to the measure of its intercepted arc. The intercepted arc is $arc \, ABC$
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