QL-L11   QG-P16-Triple Line


Each Quadrilateral has three Component Quadrigons QL-QGa, QL-QGb and QL-QGc (see QL-3QG1). QL-L11 is the line through the 3 versions of the point QG-P16 in these Component Quadrigons.
Let Co-a be the Conic(QL-P1,vertices QL-QGa), Co-b be the Conic(QL-P1,vertices QL-QGb) and Co-c be the Conic(QL-P1,vertices QL-QGc).
Let QG-P16a be the point QG-P16 in QL-QGa, QG-P16b be the point QG-P16 in QL-QGb, QG-P16c be the point QG-P16 in QL-QGc.
All three conics Co-a, Co-b, Co-c have mutually three points in common and therefore they have per pair a 4th intersection point.
It appears that QG-P16a is the 4th intersection point of Co-b and Co-c, QG-P16b is the 4th intersection point of Co-c and Co-a, QG-P16c is the 4th intersection point of Co-a and Co-b. The three points QG-P16a, QG-P16b, QG-P16c are collinear on a line with simple coordinates and some special properties.
See Ref-66, QPG-messages #1015-#1021.

QL L11 QG P16 Triple Line 01

1st CT-coordinate

    b2c2 l (m-n) (2 a2 (l - m) (n - l) + b2 (l - m) (m - n) + c2 (n - l) (m - n))

Properties
• These points lie on QL-L11:
   - QL-P26 (Least Squares Point)
   - QL-Tf1(QL-P17)
   - QL-Tf1(QL-P24)
   - QL-Tf3(QL-P2.QL-P6)
   - QL-Tf3(QL-P3.QL-P4)
QL-P6 = QL-Tf3(QL-L11)
QL-L11 = QL-Tf1(QL-Ci6) (Eckart Schmidt, November 30,2012)
QL-L11 = QL-Tf6(QL-P1)
QL-L11 is the perpendicular bisector of QL-P1.QL-Tf1(QL-P6)