QA-P36: Complement of QA-P30 wrt the QA-Diagonal Triangle

QA-P36 is the Complement of QA-P30 (Reflection of QA-P2 wrt the QA-Diagonal Triangle) wrt the Diagonal Triangle.

1st CT-Coordinate

16 Δ² p² q r (p + q) (p + r) (q + r) (b² (p + q) r – c² q (p + r)) (a² (-q + r) + (b² – c²) (q + r)) +

2 ((b² – c²) p (q – r) – a² (2 q r + p (q + r))) (c⁴ p q (p + r) (q + r) – c² p q r (a² (p + r) + b² (q + r)) +

(p + q) r (a⁴ q (p + r) + b⁴ p (q + r) – 2 a² b² p q)) (-(c² q + b² r) p² (q + r) + a² q r (p² + q r))

1st DT-Coordinate

(b² S_B r² + c² S_C q² – b² c² p²) (a² (SA p² + SB q² + SC r²) – 2 S² p²)

Properties

• QA-P36 lies on these QA-lines:
  • QA-P2.QA-P12          ( 1 : 1 => QA-P36 = Midpoint QA-P2.QA-P12)
  • QA-P10.QA-P30        (-1 : 3 => QA-P36 = Complement of QA-P30)
  • QA-P13.QA-P29        (-1 : 2 => QA-P36 = Reflection of QA-P29 in QA-P13)
• QA-P36 lies on QA-Ci2 (QA-DT-Nine-point Circle).
• QA-P36 is the Center of the circumscribed orthogonal hyperbola of the QA-Diagonal Triangle through QA-P2 and QA-P12.
• QA-P36 lies on the Simson Line (QA-P6.QA-P36) of QA-P2 occurring on the circumcircle of the QA-Diagonal Triangle.
• QA-P36 is QA-P2 (Euler-Poncelet Point) of the Quadrangle formed by the vertices of the QA-Diagonal Triangle and QA-P2.
• The QA-Orthopole(QA-Tf3) of QA-P36 is the Midpoint (QA-P11.QA-P23).

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