Παρασκευή, 9 Δεκεμβρίου 2011

LOCUS


Generalization of Hyacinthos Message 10485


Let ABC be a triangle Q1, Q2 two fixed points and P a variable point. Let L1,L2,L3 be the parallels through P to AQ2, BQ2, CQ2, respectively.

Ab := L2 /\ (Parallel to BQ1 through A)
Ac := L3 /\ (Parallel to CQ1 through A)

Similarly:

Bc := L3 /\ (Parallel to CQ1 through B)
Ba := L1 /\ (Parallel to AQ1 through B)

Ca := L1 /\ (Parallel to AQ1 through C)
Cb := L2 /\ (Parallel to BQ1 through C)

Which is the locus of P such that the Euler Lines of AAbAc, BBcBa, CCaCb are concurrent?

APH, 9 December 2011

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