QL-P16: QL-Quasi Circumcenter


QL-P16 is the perspector of the QL-Diagonal Triangle and the Triangle formed by the points QG-P5 (QG-1st Quasi Circumcenter) of the 3 QL-Quadrigons.
QL-P16 is also the perspector of the QL-Diagonal Triangle and the Triangle formed by the points QG-P9 (QG-2nd Quasi Circumcenter) of the 3 QL-Quadrigons.
 
QL-P16-Quasi Circumcenter-01
 
Coordinates:
1st CT-coordinate:
m n (32 a2 Δ2 (l - m) (l - n) (l m - l n + m n) (-l m + l n + m n) (-m n + l m + l n)
- (a2 m n (l - m) (l - n) + b2 l n (m - l) (m - n) + c2 l m (n - l) (n - m))
* (4 a4 l2 (l m + l n - m n) - a4 (l m + l n - m n)2 - b4 (l m - l n + m n)2 - c4 (-l m + l n + m n)2
     + 2 b2 c2 (l2 m2 - 2 l2 m n + l2 n2 + m2 n2)
     + 2 a2 b2 (2 l3 m - 3 l2 m2 - 2 l3 n + 2 l2 m n + l2 n2 - 2 l m n2 + m2 n2)
     + 2 a2 c2 (-2 l3 m + l2 m2 + 2 l3 n + 2 l2 m n - 2 l m2 n - 3 l2 n2 + m2 n2)))

1st DT-coordinate:
            a2 (Sc l2 - b2 m2 + Sa n2) (Sb l2 + Sa m2 - c2 n2)

Properties:
        QL-P1.QL-P10           (-1 : 2 => QL-P16 = Reflection of QL-P10 in QL-P1)

 

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