QG-L1: The 3rd diagonal


The 3rd diagonal of a Quadrigon is the connecting line of S1 and S2, where S1 and S2 are the intersection points of the opposite sides of the Reference Quadrigon.

QG-L1-3rdDiagonal-01

Coefficients:
CT-Coefficients QG-L1 in 3 QA-Quadrigons:
  • (-q r : p r : p q)
  • (q r : -p r : p q)
  • (q r : p r : -p q)
CT-Coefficients QG-L1 in 3 QL-Quadrigons:
  • (0 : m : n)
  • ( l : 0 : n)
  • ( l : m : 0)
DT-Coefficients QG-L1 in 3 QA-Quadrigons:
  • (0 : 1 : 0)
  • (1 : 0 : 0)
  • (0 : 0 : 1)
DT-Coefficients QG-L1 in 3 QL-Quadrigons:
  • (0 : 1 : 0)
  • (1 : 0 : 0)
  • (0 : 0 : 1)

Properties:
  • These points lie on QG-L1: QG-P2, QG-P3, QG-P17, QG-2P2a, QG-2P2b, QG-3Pa, QG=3Pb.
  • The three 3rd Diagonals in the QA-environment form the QA-Diagonal Triangle.
  • The three 3rd Diagonals in the QL-environment form the QL-Diagonal Triangle.
  • QG-L1 is the polar (see Ref-13, Polar) of any inscribed QG-conic.
  • QG-L1 is the polar (see Ref-13, Polar) of any circumscribed QG-conic.
  • QG-L1 is the QL-Tf1 image of the circle QG-Ci3.

 

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