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. 
                       
 QA-P33 Centroid Orthocenter Quadrangle
Coordinates: 
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          (3 : -2)
        QA-P12.QA-P14        (3 : -1 => QA-P33 =Complem. of QA-P12 wrt QA-Tr3)
        QA-P24.QA-P37        (1 :  1 => QA-P33 = Midpoint QA-P24.QA-P37)

 
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