QL-P9: Circumcenter QL-Diagonal Triangle

 
QL-P9 is the Circumcenter of the Diagonal Triangle (QL-Tr1) of the Reference Quadrilateral.
 
 
QL-P9-DT-Circumcenter-00
 
Coordinates: 
1st CT-coordinate:
4 m n (-4 Δ2 m2 n2 + a2 l3 (SC m + SB n) - l2 (SC m + SB n)2 + l m n (SB b2 m + SC c2 n))
where:
                   SA = (–a2 + b2 + c2)/ 2         SB = (+a2 – b2 + c2)/ 2          SC = (+a2 + b2 – c2)/ 2 
                   Δ = Area = 1/4 √[(a + b + c) (-a + b + c) (a - b + c) (a + b - c)]
 
1st DT-coordinate:
                   a2 Sa
 
 
Properties:
  • QL-P9 lies on these lines:
        QL-P2.QL-P7 =QL-L2
        QL-P8.QL-P10=QL-L7                (-1 : 3 => QL-P9 = Complement of QL-P10)

 


 

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