QG-Ci3: Quasi Isogonal Circumcircle

QG-Ci3 is the Circumcircle of QG-Tr3.
QG-Tr3 is an important triangle because the Isogonal Conjugate of this Triangle is equivalent with the Quasi Isogonal Conjugate of the Reference Quadrigon.
The 3 QA-versions as well as the 3 QL-versions of this circle coincide in one point.

QG-Ci3 in connection with Cubic QA-Cu1:

Equations:
• -c2 p q (c2 q2 - a2 q r + b2 q r + c2 q r + b2 r2) x2 + c2 (c2 p2 q2 - a2 p2 q r + b2 p2 q r + c2 p2 q r + a2 p q2 r + a2 q3 r + b2 p2 r2 + a2 q2 r2) x y - a2 c2 p q r (p + q + r) y2 + (b2 c2 p2 q2 + b2 c2 p q3 - c4 p q3 - a2 b2 p2 q r + b4 p2 q r + b2 c2 p2 q r - a4 p q2 r + b4 p q2 r + 2 a2 c2 p q2 r - c4 p q2 r - a4 q3 r + a2 b2 q3 r + b4 p2 r2 + a2 b2 p q r2 + b4 p q r2 - b2 c2 p q r2 + a2 b2 q2 r2) x z + a2 (c2 p2 q2 + c2 p q3 + c2 p q2 r + b2 p2 r2 + a2 p q r2 + b2 p q r2 - c2 p q r2 + a2 q2 r2) y z - a2 q (b2 p2 + a2 p q + b2 p q - c2 p q + a2 q2) r z2 = 0

• b2 c2 l (m - n) x2 - c2 (a2 l2 - a2 l m - b2 l m + c2 l m - a2 l n + b2 l n - c2 l n + a2 m n - c2 m n + c2 n2) x y - b2 (a2 l2 - a2 l m - c2 m n + c2 n2) x z - a2 (a2 l2 - a2 l m + c2 l m - a2 l n + b2 l n - c2 l n + a2 m n - b2 m n - c2 m n + c2 n2) y z - a2 b2 (l - m) n z2 = 0