proof of Stewart’s theorem
Let be the angle .
Cosines law on says and thus
Using cosines law on and noting that and thus we get
From the expressions above we obtain
By cancelling on both sides and collecting we are led to
and from there . Finally, we note that so we conclude that
QED
Title | proof of Stewart’s theorem |
---|---|
Canonical name | ProofOfStewartsTheorem |
Date of creation | 2013-03-22 12:38:37 |
Last modified on | 2013-03-22 12:38:37 |
Owner | Mathprof (13753) |
Last modified by | Mathprof (13753) |
Numerical id | 7 |
Author | Mathprof (13753) |
Entry type | Proof |
Classification | msc 51-00 |
Related topic | StewartsTheorem |
Related topic | ApolloniusTheorem |
Related topic | CosinesLaw |
Related topic | ProofOfApolloniusTheorem2 |