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Circle theorem proof

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Circle theorem proof

Post  karooomph on Thu Feb 26, 2009 10:59 pm

How do you prove that:

Inscribed angles subtended by the same arc of a circle are equal?

Diagram: http://i61.servimg.com/u/f61/13/61/85/57/circle12.jpg


Last edited by karooomph on Fri Feb 27, 2009 9:56 am; edited 4 times in total (Reason for editing : trying to upload pic)
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Re: Circle theorem proof

Post  bfrsoccer on Tue Mar 03, 2009 6:50 pm

Sorry, I've been away for the past five days and just got back yesterday.

Anyway, calling the intersection point (the one near the center of the circle) point E, then I think there is a theorem that says CE*AE=DE*BE, or CE/DE=BE/AE, meaning that CD is proportional to DE and BE is proportional to AE, and since angle DEA is congruent to angle CBE (I think these are called "vertical angles" - my sister is taking geometry), then triangle AED is similar to triangle BEC, and its corresponding angles, including angle a and angle b, are congruent.

I actually took a look at this yesterday too, but for some reason I was thinking that CE/AE=DE/BE, which didn't make sense (then I realized today that CE*AE=DE*BE would make sense, after looking at the picture again).
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Re: Circle theorem proof

Post  karooomph on Tue Mar 03, 2009 8:33 pm

very nice, thank you
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Re: Circle theorem proof

Post  albertwilson on Mon Jul 19, 2010 4:49 am

I am very thankful for you!

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Re: Circle theorem proof

Post  LeeRain on Mon Sep 27, 2010 11:59 am

I have been away for the past five days and just got back yesterday




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Re: Circle theorem proof

Post  nirvana on Tue Nov 02, 2010 3:18 am

UN chief attacked over 'silence' on China dissidents
By Barbara Plett BBC UN correspondent
UN Secretary General Ban Ki-moon (left) and Chinese President Hu Jintao in Beijing. Photo: 1 November 2010 Ban Ki-moon (left) has defended his low-key style during the talks with President Hu Jintao in Beijing

A human rights group has criticised UN Secretary General Ban Ki-moon for failing to raise human rights issues at talks with China's President Hu Jintao.

The New-York based Human Rights Watch had urged Mr Ban to publicly express concern about the imprisonment of Nobel Peace Prize winner Liu Xiaobo.

It said Mr Ban's silence was shocking and sent a chilling message to Chinese rights activists.

Mr Ban's spokesman confirmed the matter was not discussed at Monday's talks.

The spokesman said the question of human rights did not come up even in a private meeting with President Hu, because, he said, there were many other issues to discuss.

He said Mr Ban had asked Beijing to play a greater role in solving African conflicts such as those in Somalia and Sudan.
'Quiet diplomacy'
Liu Xiaobo in Oct 28, 2008 Liu Xiaobo: Jailed for 11 years in December 2009

Activists had already criticised the secretary-general for his cautious response when Liu Xiaobo was awarded the Nobel Peace Prize last month.

Mr Ban then offered only indirect praise for the jailed dissident then, and did not call for his release.

The UN chief has defended his low-key style by saying he likes to exercise quiet diplomacy.

But commentators say he has to tread carefully, since he needs China's support to win a second term in office.

That is because it is one of the five powerful UN Security Council members which wields a veto.

HRW said if this was indeed the secretary-general's calculation, he should remember that his relevance in the post depended on being a clear and courageous voice on human rights.







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