Math Is Fun Forum

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

In a circle the angle at the center is double the angle at the circumf

I have the following theorem : "In a circle the angle at the center is double the angle at the circumference when the angles have the same circumference as base."

(Figure is in the link) http://aleph0.clarku.edu/~djoyce/java/elements/bookIII/propIII20.html

English isn't my first language, so I just want to make sure that I understood something correctly. We prove the theorem by putting the two angles one on the other for the circumference. I was just wondering, can I assume that the angles do not need to be one on the other and they can have different portion of the circumference, as long as the circumference are of the same lenght ? (Will the proposition still work in this way?) I guess that Euclid did the proof by putting the angles one on the other for making the demonstration less wordy. (Less long to read)

Thank you!

geometry proof-verification euclidean-geometry

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: In a circle the angle at the center is double the angle at the circumf

hi Al-Allo

I proved this here:

http://www.mathisfunforum.com/viewtopic.php?id=17799

post 6.

My method is the same as Euclid's.  Maybe that will help.

Bob

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Children are not defined by school ...........The Fonz
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Sometimes I deliberately make mistakes, just to test you!  …………….Bob