Geometry

(1) Equilateral Triangles

http://euclid.ucc.ie/pages/MATHENR/MathEnrichment/2.Equilateral_Triangles.pdf

Van Schooten's and Pompeiu's Theorems

http://www.cut-the-knot.org/Curriculum/Geometry/Pompeiu.shtml

An Extension of van Schooten's Theorem

http://www.cut-the-knot.org/pythagoras/PointOnCircumcircle2.shtml

Ptolemy's Theorem

http://www.cut-the-knot.org/proofs/ptolemy.shtml

Fermat point

http://en.wikipedia.org/wiki/Fermat_point

The Fermat Point and Generalizations

http://www.cut-the-knot.org/Generalization/fermat_point.shtml