QG-Ci1: QA-DT-Thales Circle
The QA-DT-Thales Circle is the circle with the line segment between the vertices of the QA-Diagonal Triangle (QG-2P2a and QG-2P2b) that are unequal the Diagonal Crosspoint (QG-P1) as diameter.
Equations:
CT-Equation QG-Ci1 in 1st QA-Quadrigon:
q (2 c2 q - a2 r + b2 r + c2 r) x2 + p r (a2 - b2 + c2) y2 + q (a2 p + b2 p - c2 p + 2 a2 q) z2 + (-2 c2 p q + a2 p r - b2 p r - c2 p r - a2 q r + b2 q r - c2 q r) x y
+ (a2 p q - b2 p q - c2 p q + 2 a2 q2 - 2 b2 q2 + 2 c2 q2 - 2 b2 p r - a2 q r - b2 q r + c2 q r) x z + (-a2 p q + b2 p q - c2 p q - a2 p r - b2 p r + c2 p r - 2 a2 q r) y z = 0
CT-Equation QG-Ci1 in 1st QL-Quadrigon:
-2 SA l x2 + 2 SC n z2 + (a2 l - b2 l + c2 l - 2 c2 n) x y + (a2 l + b2 l - c2 l + a2 n - b2 n - c2 n) x z + (2 a2 l - a2 n + b2 n - c2 n) y z = 0
DT-Equation QG-Ci1 in 1st QA-Quadrigon:
(a2 - b2 + c2) x2 + (a2 - b2 + 3 c2) x y + 2 (a2 + c2) x z + (3 a2 - b2 + c2) y z + (a2 - b2 + c2) z2 = 0
DT-Equation QG-Ci1 in 1st QL-Quadrigon:
-b2 l2 x2 – 2 SC l2 x y - (a l - c n) (a l + c n) y2 +2 SA n2 y z + b2 n2 z2 = 0
Properties:
- QG-Ci1 is orthogonal wrt circles QG-Ci2 and QL-Ci1.
- The intersection points of QG-Ci1 with QG-Ci2 lie on the Perspective Squares double cubic QG-2Cu1.