QA-P27: M3D Center
QA-P27 is the perspector of the QA-Diagonal Triangle and the QA-M3D Triangle.
The QA-M3D Triangle (Ma.Mb.Mc in the figure) is the triangle bounded by the M3D Lines (see paragraph QL-L9) occurring in the 3 QA-Quadrigons.
Coordinates:
1st CT-Coordinate:
(q + r) (2 p + q + r) (q2 + q r + r2) (-p4 - 2 p3 q - 2 p2 q2 - p q3 - 2 p3 r + p q2 r + q3 r - 2 p2 r2 + p q r2 + q2 r2 - p r3 + q r3)
1st DT-Coordinate:
1 / ((p2 + q2 + r2)2 - 4 ((q2 + r2)2 - q2 r2))
Area of M3D Triangle (CT-coordinates):
2 Δ (p2 + p q + q2 + p r + q r + r2)2 / (3 (p + q) (p + r) (q + r) (p + q + r))
2 Δ (p2 + p q + q2 + p r + q r + r2)2 / (3 (p + q) (p + r) (q + r) (p + q + r))
Properties: