Σάββατο 6 Σεπτεμβρίου 2014

EULER LINES - PARALLELOGIC TRIANGLES - I

Let ABC be a triangle and A'B'C' the cevian triangle of P = I

Denote:

Ab = the orthogonal projection of A' on the parallel to BB' through A

Ac = the orthogonal projection of A' on the parallel to CC' through A

Similarly (cyclically) Bc, Ba and Ca,Cb.

Conjecture: ABC and The triangle bounded by the Euler lines of AAbAc, BBcBa, CCaCb are parallelogic.

Locus ?

Antreas P. Hatzipolakis. 7 September 2014

Generalization: Hyacinthos #22570

Geometrical Loci associated with the Euler Line


-
Ετικέτες ,

Δεν υπάρχουν σχόλια:

Δημοσίευση σχολίου

Εγγραφή σε: Σχόλια ανάρτησης (Atom)

ETC

X(72906) = X(2)X(3)∩X(523)X(25739) Barycentrics    -2*a^16+6*a^14*b^2-5*a^12*b^4+3*a^10*b^6-10*a^8*b^8+12*a^6*b^10-a^4*b^12-5*a^2*b^14+2*b...

  • EUCLID 4404
  • HOMOTHETIC TRIANGLES and EULER LINES
    Theorem 1. Let ABC be an equilateral triangle and P a point. The Euler lines of the triangles PBC,PCA,PAB are concurent.Denote the point ...
  • ETC
    X(5459) Let ABC be a triangle, let A', B', C' be the midpoints of BC, CA, AB. Let L_a be the perpendicular through A' ...