# Thread: circle proof

1. ## circle proof

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. ## Re: circle proof

Originally Posted by markosheehan

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

3. ## Re: circle proof

any other ideas on how to work it out . i still cant

4. ## 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

5. ## Re: circle proof

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

6. ## Re: circle proof

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

indeed I see the forest now and it is beautiful.
Thank you.

7. ## 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

8. ## Re: circle proof

Originally Posted by markosheehan
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*}

9. ## Re: circle proof

what does m stand for. i dont understand your notation how does m arcABC=mASC

10. ## 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 $arc \, ABC$