Ptolemy's theorem
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Ptolemy’s theorem
If is a cyclic quadrilateral, then the product of the two diagonals is equal to the sum of the products of opposite sides.
When the quadrilateral is not cyclic we have the following inequality
An interesting particular case is when both and are diameters, since we get another proof of Pythagoras’ theorem.
Keywords:
Quadrilateral, Circle, Cyclic, Ptolemy
Type of Math Object:
Theorem
Major Section:
Reference
Groups audience:
Mathematics Subject Classification
51-00 General reference works (handbooks, dictionaries, bibliographies, etc.)60K25 Queueing theory
18-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
68Q70 Algebraic theory of languages and automata
37B15 Cellular automata
18-02 Research exposition (monographs, survey articles)
18B20 Categories of machines, automata, operative categories
Comments
Ptolemy's thm
Maybe the word "Ptolemy" could go in the keywords; the search
engine currently finds no hits on that word.
We might mention some of the easy corollaries of Pt's thm. E.g.
if we specialize to the case in which $AC$ and
$BD$ are diameters of the given circle, we get Pythagoras's theorem.
LH