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).

Coordinates:
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 SC q2 - SB 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-P29)
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).

Vernieuwen