Schooten theorem
Theorem: Let be a equilateral triangle. If is a
point on the circumscribed circle then the equality
holds.
Proof: Let so that . Because
, the triangle is
equilateral, so . Because and
we have that the triangles
and are equivalent
. Since we have that
.
References
-
1
[Pritchard] Pritchard, Chris (ed.) The Changing Shape of Geometry
: Celebrating a Century of Geometry and Geometry Teaching. Cambridge University Press, 2003.
Title | Schooten theorem |
---|---|
Canonical name | SchootenTheorem |
Date of creation | 2013-03-22 14:05:50 |
Last modified on | 2013-03-22 14:05:50 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 7 |
Author | mathcam (2727) |
Entry type | Theorem |
Classification | msc 51-00 |
Synonym | Ptolemy’s theorem |