## Equilateral Triangles

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• Soient A ,B ,C les symetriques d un point M par rapport aux cotes BC,CA,AB d un triangle equilateral ABC. Demontrer que les droites AA ,BB ,CC sont
Message 1 of 1 , Feb 23, 2001
Soient A',B',C' les symetriques d'un point M par rapport aux cotes
BC,CA,AB d'un triangle equilateral ABC. Demontrer que les droites
AA',BB',CC' sont concourantes.
(P. Aubert - G. Papelier: Exercices de geometrie analytique... I, p. 31, #38)

Now, by changing the notation, let ABC be the reference triangle,
P a notable point on ABC plane (= O, H, I, etc), and T = A*B*C* a notable
equilateral triangle of ABC (Morley, Napoleon etc).
For every (P,T) corresponds a point (according to above).

We can also formulate loci problems:

Which is the locus of the point of concurrence as the point M, in the problem
above, moves on a given line/circle?
(Application in the reference triangle:
Equilateral triangle : Napoleon Triangle; line : Euler Line /
circle : incircle or circumcircle of ABC)

Antreas
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