Difference between revisions of "Ptolemy's Theorem"

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=== Definition ===
 
=== Definition ===
  
Given a cyclic quadrilateral <math>ABCD</math> with side lengths <math>{a},{b},{c},{d}</math> and diagonals <math>{p},{q}</math>:
+
Given a cyclic quadrilateral <math>ABCD</math> with side lengths <math>{a},{b},{c},{d}</math> and diagonals <math>{e},{f}</math>:
  
<math>ac+bd=pq</math>
+
<math>ac+bd=ef</math>

Revision as of 13:02, 18 June 2006

Ptolemy's theorem gives a relationship between the side lengths and the diagonals of a cyclic quadrilateral; it is the equality case of the Ptolemy inequality.

Definition

Given a cyclic quadrilateral $ABCD$ with side lengths ${a},{b},{c},{d}$ and diagonals ${e},{f}$:

$ac+bd=ef$

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