QL-L5: NSM Line
The NSM Line is the line through the Newton-Steiner Point (QL-P7) and the Miquel Point (QL-P1)
1st CT-coefficient
l (m – n) ((a2 – b2) b2 (l – m)2 n2 (3 l m – l n – m n) – (a2 – c2) c2 m2 (l – n)2 (l m – 3 l n + m n)
+ b2 c2 (-2 m3 n3 + 4 l m2 n2 (m + n) – 5 l2 m n (m2 + n2) + l3 (m + n) (m2 + n2)))
1st CT-Coordinate Infinity point
l m n (a2 (2 l – m – n) – (b2 – c2) (m – n))
– m (l – n) (l m – l n + m n) SB + n (l – m) (l m – l n – m n) SC
–
1st DT-coefficient
l2 (l2-m2) (l2-n2) (m2-n2) S2 + l2 (m2-n2)3 SA2 – m2 (-l2+n2)3 SB2 – (l2-m2)3 n2 SC2
+ (m2-n2) ((l2+m2) (l2-n2)2 SA SB+(l2-m2)2 (l2+n2) SA SC)
1st DT-Coordinate Infinity point:
a2 m2 n2 – SB l2 m2 – SC l2 n2
Properties
- QL-P1, QL-P7, QL-P19 lie on QL-L5.
- QL-L5 is parallel to QL-L6 (Quasi Ortholine).
- QL-L9 (M3D Line) is perpendicular to QL-L5.
- QL-L5 // Directrix of the QL-Co3-parabola.
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