QL-P22: QL-Nine-point Center Homothetic Center
QL-P22 is the homothetic Center of the Reference Quadrilateral L1.L2.L3.L4 and the homothetic Quadrilateral formed by the lines parallel to the lines L1, L2, L3, L4 through the Nine-point Centers of the corresponding component triangles.
The prefix “QL-“ has been added in the name of QL-P22 because there is also a Nine-point Homothetic Center in a Quadrangle.
(m – n) (a2 SA l2 + b2 SB l m + c2 SC l n + 8 Δ2 (l m + l n - 2 m n - l2))
(m2 - n2) ((m2 - n2)2 Sa2 + (n2 - l2)2 Sb2 + (l2 - m2)2 Sc2 - 2 S2 (3 l2 m2 + 3 l2 n2 - 5 m2 n2) + 2 (l4 Sb Sc + m4 Sa Sc + n4 Sa Sb))
- QL-P22 lies on these lines:
- QL-P22.QL-P6 // QL-P2.QL-P5 // QL-P4.QL-P20
- QL-P22 is the Midpoint of QL-P5 (Clawson Center) and QL-P20 (Orthocenter Homothetic Center).
- The distance ratios between points QL-P20, QL-P22, QL-P12, QL-P5 are 3 : 1 : 2.