QG-2P5a and QG-2P5b are the intersection points of QG-Ci2 with the Diagonals of the Reference Quadrigon..
QG-Ci2 is the circle with the line segment of the side of the QL-Diagonal Triangle opposite the Diagonal Crosspoint QG-P1 as diameter.
Coordinates:
CT-coordinates QG-2P5a/b in 1st QA-Quadrigon:
QG-2P5a: (c2 p3 - a2 p r2 : c2 p (p - r) (2 q + r) + r (-a2 (p + 2 q) (p - r) + b2 p (p + 2 q + r)) : -c2 p2 r + a2 r3)
QG-2P5b: (c2 p3 - a2 p r2 : p r (b2 (-p + r) + a2 (p + r) - c2 (p + r)) : c2 p2 r - a2 r3)
DT-coordinates QG-2P5a/b in 1st QA-Quadrigon:
QG-2P5a: (-2 c2 p4 + 2 SB p3 r + 2 SB p2 r2 - 2 a2 p r3 : c2 p4 - 2 c2 p3 r - (a2 - c2) p2 r2 + 2 a2 p r3 - a2 r4 : 2 c2 p3 r - 2 SB p2 r2 - 2 SB p r3 + 2 a2 r4)
QG-2P5b: (2 c2 p4 + 2 SB p3 r - 2 SB p2 r2 - 2 a2 p r3 : -c2 p4 - 2 c2 p3 r + (a2 - c2) p2 r2 + 2 a2 p r3 + a2 r4 : 2 c2 p3 r + 2 SB p2 r2 - 2 SB p r3 - 2 a2 r4)
CT-coordinates QG-2P5a/b in 1st QL-Quadrigon:
QG-2P5a: (-m n ((b2 (-l + m) + c2 (l - n)) (m - n) - a2 (-m n + l (m + n))) : l n (-b2 m2 + c2 n2) : l m (b2 m2 - c2 n2))
QG-2P5b: (m (-a2 l2 + b2 m2) n : l (a2 l2 - b2 m2) n : -l m (a2 (l - m) (l - n) - b2 (l - m) (m - n) + c2 (l m - l n - m n)))
DT-coordinates QG-2P5a/b in 1st QL-Quadrigon:
QG-2P5a: (0 : SC : SB)
QG-2P5b: (SB : SA : 0)
Properties:
- QG-2P5a and QG-2P5b are collinear with QG-P18
- QG-2P5a and QG-2P5b lie on these circles:
– QG-Ci2: QL-DT-Thales Circle
– QL-Ci2: Medial Circle QL-Diagonal Triangle
- QG-2P5a and QG-2P5b lie on these cubics:
– QG-2Cu1 a/b: Perspective Squares Double Cubic
– QL-Cu1: QL-Quasi Isogonal Cubic