QA-P30: Reflection of QA-P2 in QA-P11

QA-P30 is the Reflection of QA-P2 (Euler-Poncelet Point) in QA-P11 (Circumcenter Diagonal Triangle).

1st CT-Coordinate

(2 a⁴ q r (p + q) (p + r) + b⁴ p r (q + p) (q + r) + c⁴ p q (r + p) (r + q)

– b² c² p (q + r) (p q + p r + 2 q r) + a² b² p (p + q) (r – 3 q) r + a² c² p q (q – 3 r) (p + r)) *

(a⁴ q r (p + q) (p + r) (p q + p r – 2 q r) + b⁴ p r (q + p) (q + r) (p q + 2 p r – q r) +

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

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

1st DT-Coordinate

1/(c² b² p² – c² S_C q² – S_B b² r²)

Properties

• QA-P30 lies on these QA-lines:
  • QA-P2.QA-P11          ( 2 : -1 => QA-P30 = Reflection of QA-P2 in QA-P11)
  • QA-P10.QA-P36        (-2 :  3 => QA-P30 = Complement of QA-P36)
  • QA-P12.QA-P29        ( 2 : -1 => QA-P30 = Reflection of QA-P12 in QA-P28)
  • QA-P13.QA-P35        ( 5 : -4)
• QA-P30 is the Involutary Conjugate of QA-P6 (Parabola Axes Crosspoint).
• QA-P30 lies on the circumcircle of the Diagonal Triangle (QA-Ci1).
• QA-P30 is the Antipode of QA-P12 in the QA-DT-P3-P12 Orthogonal Hyperbola (QA-Co4).

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