nL-n-Luc3 nL-Sum of Vectors Point


Morley introduced this technique: vectors can be constructed from a fixed origin (nL–n–P3) to the (n–1)L versions of another point. The endpoint of the sum of these vectors defines a new central nL-point. This method is used for nL-n-P7.

The construction is sometimes abbreviated as SVP (Sum Vector Point).

Application in a 4-Line
  • There exists a QL-point X on the line QL-L4 for which the Sum Vector of X.H1, X.H2, X.H3, X.H4 equals QL-P3. This point corresponds to QL-P2.QL-P3 (-1 : 4), and also to QL-P12.QL-P27 (-3:4).
  • (Here, H1, H2, H3, H4 are the orthocenters of the four Component Triangles of the QL.)
  • See [34], QFG#850.



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