122

Geometriae Dedicata

Springer

1998

71

2

179-208

Ceva . , Menelaus , selftransversality , transversal , polygon , cyclic product

براي دانلودو مشاهده مقاله به قسمت لينكهاي مرتبط مراجعه نماييد

The theorems of Ceva and Menelaus are concerned with cyclic products of ratios of lengths of collinear segments of triangles or more general polygons. These segments have one endpoint at a vertex of the polygon and one at the intersection point of a side with a suitable line. To these classical results we have recently added a lsquoselftransversality theoremrsquo in which the lsquosuitable linersquo is determined by two other vertices. Here we present additional lsquotransversalityrsquo properties in which the lsquosuitable linersquo is determined either by a vertex and the intersection point of two diagonals, or by the intersection points of two pairs of such diagonals. Unexpectedly it turns out that besides several infinite families of systematic cases there are also a few lsquosporadicrsquo cases.

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