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April 30th, 2012, 10:57 PM   #1
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Circle properties

Are the angles in opposite segments of a cyclic quadrilateral in a semicircle supplementary? If so, how do we prove it?
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May 1st, 2012, 12:34 AM   #2
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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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