QL-P15: 2nd QL-Quasi Centroid
QL-P15 is the Centroid of the triangle formed by the three 2nd Quasi Centroids (QG-P8) in a Reference Quadrilateral.
The prefix QL- has been added in the name of QL-P15 because there is also a 2nd Quasi Centroid in a Quadrangle.
(m - n) (l5 m3 - 2 l4 m4 - l5 m2 n - 2 l4 m3 n + 6 l3 m4 n - l5 m n2 + 8 l4 m2 n2 - 9 l3 m3 n2 + l5 n3 - 2 l4 m n3 - 9 l3 m2 n3 + 20 l2 m3 n3 - 10 l m4 n3 - 2 l4 n4 + 6 l3 m n4 - 10 l m3 n4 + 6 m4 n4)
(m2- n2) (l4 - 3 l2 m2 + 3 l2 n2 + 5 m2 n2)
- QL-P15 lies on this line:
- QL-P15 is the Reflection of QL-P14 (1st QL-Quasi Centroid) in QL-P12 (Lateral Centroid).
- QL-P15 is the Centroid of the Triangle formed by the 3 QL-versions of QG-P10 (note Eckart Schmidt).
- QL-P15 is the Centroid of the Triangles formed by the 3 QL-versions of QG-P2, QG-P4, QG-P8 (all Centroid related points).
- The 3 versions of QL-P15 in a Quadrangle are collinear.