Nikolas Dergiades, A synthetic proof and generalization of Bellavitis' theorem,
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.

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