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April 30th, 2012, 10:57 PM  #1 
Newbie Joined: Apr 2012 Posts: 1 Thanks: 0  Circle properties
Are the angles in opposite segments of a cyclic quadrilateral in a semicircle supplementary? If so, how do we prove it?

May 1st, 2012, 12:34 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Circle properties
Yes, the opposite angles in a cyclic quadrilateral are supplementary, and the converse is also true. For a proof, see Euclid's The Elements, Book III, propositions 21 and 22. 

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