QA-P39 Midpoint of QA-P12 and QA-P20

 
QA-P39 is the Midpoint of QA-P12 and QA-P20.
 
QA-P39-Midpoint QA-P12 and QA-P20-01
Coordinates: 
1st CT-Coordinate:
                   4 S2 p q r (q + r) (2 p + q + r) (-p2 + q r - p q - p r)
                   + 2 (p + q + r) (a2 (2 q r + p q + p r) - (b2 - c2) p (q - r)) (a2 q r (p2 + q r) - b2 p2 r (q + r) - c2 p2 q (q + r))
 
1st DT-Coordinate:
a4 p2 (-p2 + q2 + r2) + a2 (b2 + c2) (p4 - (q2 - r2)2) - (b2 - c2)2 (p2 (q2 + r2) - (q2 - r2)2)
 
 
Properties:
  • Given Bimedians M12*M34, M13*M24, M14*M23 of the Reference Quadrangle. Let T1.T2.T3 be the Euler Triangle of the Diagonal Triangle S1.S2.S3.  The corresponding lines parallel to the Bimedians through T1, T2 and T3 concur in QA-P39 (Seiichi Kirikami, September 30, 2012).  For explanation “Bimedian” and “Euler Triangle” see Ref-13.

 

Add a comment


Antispam code
Renew