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Pascal-points quadrilaterals inscribed in a cyclic quadrilateral
Published online by Cambridge University Press: 06 June 2019
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]:–
(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)
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