QL-L5: NSM Line


The NSM Line is the line through the Newton-Steiner Point (QL-P7) and the Miquel Point (QL-P1)
 
QL-L5-NSM Linet-00

Coefficients/Coordinates:
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
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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: