QA-P24: Anticomplement of QA-P1 wrt the Morley Triangle

QA-P24 is the AntiComplement of QA-P1 wrt the Morley Triangle (QA-Tr3).

1st CT-Coordinate

(q T_B + r T_C) ((q + r)T_A + (p + r)T_B + (p + q)T_C )

–2 q r (T_B + T_C)² – 4 T_B T_C (r (p + r) + q (p + q))

where:

T_A = (q + r) S_A T_B = (p + r) S_BT_C = (p + q) S_C

1st DT-Coordinate

(p² – (q + r)²) (p² – (q – r)²) S_B S_C – 4 (-a⁴ q² r² + b² S_C p² r² + c² S_B p² q²)

Properties

• QA-P24 lies on this QA-line:
  • QA-P1.QA-P14       (3 : -2 => QA-P24 = AntiCompl. of QA-P1 wrt QA-Tr3)
  • QA-P33.QA-P37     (-1 : 2 => QA-P24 = Reflection of QA-P37 in QA-P33)
  • QL-P2.QG-P5          (-1 : 2 => QA-P24 = Reflection QG-P5 in QL-P2)
• QA-P24 is the Homothetic Center of the Morley Triangle and the 1st Quasi Circumcenter (QG-P5) Triangle.
• QA-P24 is the Perspector of the QG-P5 Triple Triangle and the QL-P2 Triple Triangle (see QA-Tr-1).
• QA-P24 is the Orthology Center of the QG-P6 Triple Triangle wrt the Triple triangles of QG-P1/QG-P2/ QG-P4/QG-P8/QG-P15/QL-P12. See QA-Tr-1. See [34], QFG#962,#963.

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