## Eight Point Conic General 1As shown by John Rigby in the Problem Corner of the Mathematical Gazette, July 2007, pp. 358-362, the result still holds if the pairs of lines PE and PG, and PF and PH, are respectively EQUI-INCLINED towards the OPPOSITE SIDES of ABCD (i.e. angle PEA = angle PGD; angle PFC = angle PHD). Drag A, B, C or D, as well as E and F onto the extensions of the sides - also check when ABCD becomes a crossed quadrilateral. ## Eight Point Conic General 2As shown by John Rigby in the Problem Corner of the Mathematical Gazette, July 2007, pp. 358-362, the result actually generalizes further to ANY quadrilateral ABCD if the pairs of lines PE and PG, and PF and PH, are respectively EQUI-INCLINED towards the DIAGONALS of ABCD (i.e. angle BPE = angle CPG; angle CPF = angle DPH).
Drag A, B, C or D, as well as E and F onto the extensions of the sides - also check when ABCD becomes a crossed quadrilateral. {When ABCD is cyclic, this general condition is equivalent to the pairs of lines PE and PG, and PF and PH, respectively equi-inclined towards the opposite sides of ABCD.} For information on the Mathematical Gazette go to The Mathematical Gazette Created by Michael de Villiers, 9 March 2008 with Cinderella |