Nikolas Dergiades, A synthetic proof and generalization of Bellavitis'
Forum Geometricorum, 6 (2006) 225--227.
Abstract: In this note we give a synthetic proof of Bellavitis' theorem and
then generalizing this theorem, for not only convex quadrilaterals,
we give a synthetic geometric proof for both theorems direct and converse,
as Eisso Atzema proved, by trigonometry, for the convex case (E. J. Atzema,
Forum Geom, 6 (2006) 181--185). From this approach evolves clearly the connection
between hypothesis and conclusion.