Schooten theorem

Theorem: Let ABC be a equilateral triangleMathworldPlanetmath. If M is a point on the circumscribed circle then the equality



Proof: Let B(MA) so that MB=BB. Because BMA^=BCA^=60, the triangleMathworldPlanetmath MBB is equilateral, so BB=MB=MB. Because AB=BC,BB=BM and ABB^MBC^ we have that the triangles ABB and CBM are equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath. Since MC=AB we have that AM=AB+BM=MC+MB.


  • 1 [Pritchard] Pritchard, Chris (ed.) The Changing Shape of GeometryMathworldPlanetmath : 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