QG-P12: Inscribed Harmonic Conic Center
The Inscribed Harmonic Conic Center is the Center of the Inscribed Harmonic Conic QG-Co1. This conic touches the sidelines of the Quadrigon in their perspective midpoints.
See picture below.
Coordinates:
CT-Coordinates QG-P12 in 3 QA-Quadrigons:
- (p(2p+q+r) : q(p-r) : r(p-q))
- (p(r-q) : q (r-p) : r(p+q+2r))
- (p(q-r) : q(p+2q+r) : r(q-p))
CT-Coordinates QG-P12 in 3 QL-Quadrigons:
- ( m + n : -2l + n : -2l + m)
- (-2m + n : l + n : -2m + l)
- ( -2n + m : -2n + l : l + m)
CT-Area of QG-P12–Triangle in the QA-environment:
- p q r (p + q)(p + r)(q + r) Δ / ((p2 + p q + p r - q r) (p q + q2 - p r + q r) (p q - p r - q r - r2))
CT-Area of QG-P12–Triangle in the QL-environment:
- 0 (points are collinear on Newton Line)
DT-Coordinates QG-P12 in 3 QA-Quadrigons:
- (-p2 : q2 : r2)
- ( p2 : -q2 : r2)
- ( p2 : q2 : -r2)
DT-Coordinates QG-P12 in 3 QL-Quadrigons:
- (-2 m2 n2 : l2 n2 : l2 m2)
- ( m2 n2 : -2 l2 n2 : l2 m2)
- ( m2 n2 : l2 n2 : -2 l2 m2)
DT-Area of QG-P12–Triangle in the QA-environment:
- (-2 S p2 q2 r2) / ((-p2+q2+r2) (p2+q2-r2) (p2-q2+r2))
DT-Area of QG-P12–Triangle in the QL-environment:
- 0 (points are collinear on Newton Line)
Properties: