QL-P21: Adjunct Orthocenter Homothetic Center
QL-P21 is the Perspector of
- the Quadrilateral formed by the lines parallel to the lines L1, L2, L3, L4 through the Orthocenters of the corresponding component triangles and
- the Quadrilateral formed by the lines perpendicular to the lines L1, L2, L3, L4 through the Orthocenters of the corresponding component triangles.
Coordinates:
1st CT-Coordinate
2 a2 (a4 + (b2 - c2)2 - 2 a2 (b2 + c2)) (l - m)2 m (l - n)2 (m - n) n
+ 2(-m + n) (a2 m n (l - m) (l - n) + b2 l n (m - l) (m - n) + c2 l m (n - l) (n - m)) (2 a2 (b2 m (l - n) + c2 n (l - m))
+ a4 (-l2 + m n) + (b2 - c2)(b2 (l2 - 2 l m + m n) - c2 (l2 - 2 l n + m n)))
1st DT-coordinate:
Tl (Sa3 Tl4 + Sb3 Tm4 + Sc3 Tn4
+ 2 (m2 + n2) Sa Sb Sc Tm Tn (Tn - Tm)
+ Sa2 Tl2 ((m2 + 3 n2) Sb Tm - (3 m2 + n2) Sc Tn)
+ Sc2 Tn2 (Sb Tm (Tl + 3 Tm) + Sa (3 l2 Tl - 2 n2 Tl - 3 m2 Tn + m2 Tm))
+ Sb2 Tm2 (Sc Tn (Tl + 3 Tn) + Sa (3 n2 Tm + 2 m2 Tl - 3 l2 Tl - n2 Tn)))
where:
Tl = m2 - n2 Tm = n2 - l2 Tn = l2 - m2
Properties:
- QL-P21 lies on this line: