QL-P20: Orthocenter Homothetic Center

QL-P20 is the homothetic Center of the Reference Quadrilateral L1.L2.L3.L4 and the Quadrilateral formed by the lines parallel to the lines L1, L2, L3, L4 through the Orthocenters of the corresponding component triangles.

1^st CT-Coordinate

(m – n) (a² S_A m n – b² S_B l m – c² S_C l n + S_B S_C (l² + m n))

or

(m – n) (S_B S_C l² – b² S_B l m – c² S_C l n + 4 Δ² m n)

1^st DT-coordinate

(m²-n²) ((-a² l²+b² m²+c² n²)² – 4 Sa² m² n²)

Properties

• QL-P20 lies on these lines:
  • QL-P1.QL-P21 = QL-L5               (1 : 1 => QL-P20 = Midpoint of QL-P1, QL-P21)
  • QL-P5.QL-P7   = QL-L1
• QL-P19.QL-P20 // QL-P7.QL-P21
• QL-P20 is the Reflection of QL-P5 (Clawson Center) in QL-P22 (QL-Nine-point Center Homothetic Center).
• The distance ratios between points QL-P20, QL-P22, QL-P12, QL-P5 are 3 : 1 : 2.
• QL-P20 is the Center of the 5^th line conic (QL-Co-1) of QL-L2 (Eckart Schmidt, July, 2012).

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