• DOI:10.1017/mag.2019.54
• Corpus ID: 233360695

Pascal-points quadrilaterals inscribed in a cyclic quadrilateral

@article{Fraivert2019PascalpointsQI,
  title={Pascal-points quadrilaterals inscribed in a cyclic quadrilateral},
  author={David Fraivert},
  journal={The Mathematical Gazette},
  year={2019},
  volume={103},
  pages={233 - 239}
}

• David Fraivert
• Published 1 July 2019
• Mathematics
• The Mathematical Gazette

This paper presents some new theorems about the Pascal points of a quadrilateral. We shall begin by explaining what these are. Let ABCD be a convex quadrilateral, with AC and BD intersecting at E and DA and CB intersecting at F. Let ω be a circle through E and F which meets CB internally at M and DA internally at N. Let CA meet ω again at L and let DB meet ω again at K. By using Pascal’s theorem for the crossed hexagons EKNFML and EKMFNL and which are circumscribed by ω, the following results can be proved [1]:– (a) NK, ML and AB are concurrent (at a point P internal to AB)(b) NL, KM and CD are concurrent (at a point Q internal to CD)