A Generalization of Stewart's Theorem (1940)
From point P construct equi-inclined lines to the sides (or their extensions) of quadrilateral ABCD to form a Miquel quadrilateral. Repeat the same process from P to the Miquel quadrilateral, and three times more. Then the Miquel quadrilateral A4B4C4D4 is similar to quadrilateral ABCD.
A generalization of Neuberg's Theorem to polygons
Reference to Stewarts's Theorem (involving perpendiculars to the sides)
Stewart, B.M. (1940). Cyclic Properties of Miquel Polygons. Am. Math. Monthly, Vol. 47 (Aug-Sept.), pp. 462-466.
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Created by Michael de Villiers, March 2009. Modified 22 April 2020.