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 :–
- (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)