Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-20T08:49:38.406Z Has data issue: false hasContentIssue false
  • English
  • Français

Pascal-points quadrilaterals inscribed in a cyclic quadrilateral

Published online by Cambridge University Press:  06 June 2019

David Fraivert
David Fraivert*
Affiliation:
Department of Mathematics, Shaanan College, P.O. Box 906, Haifa 26109, Israel e-mail: davidfraivert@gmail.com
Get access Rights & Permissions [Opens in a new window]

Extract

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]:–

  1. (a) NK, ML and AB are concurrent (at a point P internal to AB)

  2. (b) NL, KM and CD are concurrent (at a point Q internal to CD)

Type
Articles
Information
The Mathematical Gazette , Volume 103 , Issue 557 , July 2019 , pp. 233 - 239
Copyright
© Mathematical Association 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Fraivert, D., The theory of a convex quadrilateral and a circle that forms Pascal points − the properties of Pascal points on the sides of a convex quadrilateral, Journal of Mathematical Sciences: Advances and Applications 40 (2016) pp. 1-34, accessed January 2019 at: http://dx.doi.org/10.18642/jmsaa_7100121666Google Scholar
Fraivert, D., Properties of a Pascal points circle in a quadrilateral with perpendicular diagonals, Forum Geometricorum, 17 (2017) pp. 509-526. http://forumgeom.fau.edu/FG2017volume17/FG201748.pdfGoogle Scholar