QA-P33: Centroid of the Orthocenter Quadrangle


QA-P33 is the QA-Centroid of the quadrangle formed by the Orthocenters of the Component Triangles of the Reference Quadrangle.

Infovisual QA-P33-infovisual-cvt-01.png
1st CT-Coordinate

+a4 q2 r2 – SB c2 p2 q2 – SC b2 p2 r2 + p q r (3 SB SC (p + q + r) + S2 p)

1st DT-Coordinate

S2 p4 + 2 a4 q2 r2 – (S2 + 2 SB c2) p2 q2 – (S2 + 2 SC b2) p2 r2

Properties
  • QA-P33 lies on these QA-lines:
  • QA-P1.QA-P32.QA-P33 // QA-P2.QA-P4.QA-P6 = QA-L2.
  • QL-P2 is the Centroid of the QL-Triangle formed by the 3 QL-versions of QA-P33 (note Eckart Schmidt).
  • The QA-Orthopole(QA-Tf3) of QA-P33 is a point on the line QA-P23.QA-P33 (ratio -1 : 3).
  • The area of the Orthocenter Quadrangle equals the area of the Reference Quadrangle.



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