QL-L7: Euler Line of QL-Diagonal Triangle


QL-L7 is the Euler Line of the QL-Diagonal Triangle.
QL-L7-DT-Eulerline-00

Coefficients: 
1st CT-coefficient:
l (m3 n3 SA (n2 (SA + SB) - m2 (SA + SC)) + 3 l3 (m2 - n2) (n SB + m SC) (-2 m n SA + n2 (SA + SB) + m2 (SA + SC)) + l2 m n (-n4 (3 SA2 + SA SB - 2 SB 2) + 7 m2 n2 SA (SB - SC) - 3 m3 n (2 SA2 + SA (SB - SC) + (SB - SC) SC) + m4 (3 SA2 + SA SC - 2 SC 2) + 3 m n3 (2 SA2 + SA (-SB + SC) + SB (-SB + SC))) - l4 (m - n) (n3 (SA (SB + SC) + SB (3 SB + SC)) +m2 n (-SA (SB + SC) + SC (3 SB + SC)) + m n2 (-SA (SB + SC) + SB (SB + 3 SC)) + m3 (SA (SB + SC) + SC (SB + 3 SC))) + l m2 n2 (n3 (2 SA2 + 3 SA SB + SB 2) - m3 (2 SA2 + 3 SA SC + SC 2) - m n2 (6 SA2 + SB SC + SA (4 SB + SC)) + m2 n (6 SA2 + SB SC + SA(SB + 4 SC))))
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1st DT-coefficient:
            SA (SB-SC)

Properties:
  • Quadrilateral points QL-P8 (Centroid DT), QL-P9 (Circumcenter DT), QL-P10 (Orthocenter DT) and QL-P11(Nine-point Center DT) lie on this line.
  • The ratio of distances between QL-P9, QL-P8, QL-P11, QL-P10 in this order is 2 : 1 : 3.

 

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