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.
 
 QA-P36-Complement of QA-P30 wrt QA-DT
 
Coordinates: 
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 SB r2 + c2 SC 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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