QL-P7: Newton-Steiner Point


The Newton-Steiner Point is the intersection point of the two most prominent Quadrilateral Lines: QL-L1 The Newton Line and QL-L2 The Steiner Line.
 
QL-P7-Newton-Steiner Point-00

Coordinates:
1st CT-coordinate:
-a2 m2 n2 + SB l m2 (3 n - l) + SC l n2 (3 m - l) + a2 l m n (l - m - n)
1st DT-coordinate:
            a2 l2 (m2+n2) - 2 a2 m2 n2 - (m2-n2) (b2 m2-c2 n2)

Properties:

  • QL-P7 lies on these lines:
        QL-P1.QL-P19=QL-L5    (2 : -1 => QL-P7 = Reflection QL-P1 in QL-P19)
        QL-P2.QL-P9 =QL-L2   
        QL-P5.QL-P12=QL-L1
 

 

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