QL-P16: QL-Quasi Circumcenter
QL-P16 is the perspector of the QL-Diagonal Triangle and the Triangle formed by the points QG-P5 (QG-1st Quasi Circumcenter) of the 3 QL-Quadrigons.
QL-P16 is also the perspector of the QL-Diagonal Triangle and the Triangle formed by the points QG-P9 (QG-2nd Quasi Circumcenter) of the 3 QL-Quadrigons.
m n (32 a2 Δ2 (l - m) (l - n) (l m - l n + m n) (-l m + l n + m n) (-m n + l m + l n)
- (a2 m n (l - m) (l - n) + b2 l n (m - l) (m - n) + c2 l m (n - l) (n - m))
* (4 a4 l2 (l m + l n - m n) - a4 (l m + l n - m n)2 - b4 (l m - l n + m n)2 - c4 (-l m + l n + m n)2
+ 2 b2 c2 (l2 m2 - 2 l2 m n + l2 n2 + m2 n2)
+ 2 a2 b2 (2 l3 m - 3 l2 m2 - 2 l3 n + 2 l2 m n + l2 n2 - 2 l m n2 + m2 n2)
+ 2 a2 c2 (-2 l3 m + l2 m2 + 2 l3 n + 2 l2 m n - 2 l m2 n - 3 l2 n2 + m2 n2)))
a2 (Sc l2 - b2 m2 + Sa n2) (Sb l2 + Sa m2 - c2 n2)
- QL-P16 lies on this line:
- QL-P16.QL-P9 // QL-P1.QL-P11.
- QL-P16 lies on the circumcircle of QL-Ci1, the QL-Diagonal Triangle.
- QL-P16 lies on the circumcircles of triangles formed by the 3 QL-versions of QG-P1, QG-P5 as well as QG-P9.
- QL-P16 is Railway Watcher (see QL-L-1) of lines QL-L5 (NSM Line) and QL-L6 (Quasi OrthoLine).