Σάββατο 14 Σεπτεμβρίου 2013

PRIZE (Re: ORTHOCENTER - REFLECTIONS - CONCURRENT CIRCLES)

[APH]: In fact we can take any point P (instead of H) and any points O1,O2,O3 on the circumcircles of PBC,PCA,PAB, resp.

Then the circumcircles of the triangles

AO2O3, BO3O1, CO1O2

are concurrent.

Anopolis #850

For a proof I offer the book:

R. G. SANGER: SYNTHETIC PROJECTIVE GEOMETRY (1939)

APH

-
Ετικέτες ,

1 σχόλιο:

Εγγραφή σε: Σχόλια ανάρτησης (Atom)

ETC pm

X(66901) = X(2) OF THE CEVIAN TRIANGLE OF X(290) Barycentrics    a^2*(a^2*b^2 - b^4 + a^2*c^2 - c^4)*(a^8*b^4 - 2*a^6*b^6 + a^4*b^8 - 2*a...

  • EUCLID 4404
  • PANAKIS' PSEUDOISOSCELES TRIANGLE
    Let ABC be a trangle and D1, D2, D3 the feet of the internal angle bisectors [D1D2D3 = the cevian triangle of the incenter I] Prove that th...
  • A PROOF OF MORLEY THEOREM
    Thanasis Gakopoulos - Debabrata Nag, Morley Theorem ̶ PLAGIOGONAL Approach of Proof Abstract: In this work, an attempt has been made b...