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.
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-P7 is the Midpoint of the Plücker Points QL-2P1a and QL-2P1b.
- QL-P7.QL-P1 // QL-P2.QL-P10
- QL-P7 is the Reflection of QL-P1 in QL-P19.
- The Clawson-Schmidt Conjugates (QL-Tf1) of QL-P7 lies on QL-Ci3 (Miquel Circle).
- QL-P1 lies on the Polar (see Ref-13, Polar) of QL-P7 wrt QL-Co1.