Παρασκευή 26 Απριλίου 2013

SIX CONCYCLIC CIRCUMCENTERS

Let ABC be a triangle, P a point, A'B'C' the cevian triangle of P wrt ABC and A"B"C" the cevian triangle of P wrt A'B'C' (ie A" = AA' /\ B'C' etc).

Denote:

A* = BC" /\ CB"

B* = CA" /\ AC"

C* = AB" /\ BA"

For which points P the circumcenters of the six triangles:

PA*B", PA*C", PB*C",PB*A", PC*A", PC*B" are concyclic?

Antreas P. Hatzipolakis, 26 April 2013

Δεν υπάρχουν σχόλια:

Δημοσίευση σχολίου

REGULAR POLYGONS AND EULER LINES

Let A1A2A3 be an equilateral triangle and Pa point. Denote: 1, 2, 3 = the Euler lines of PA1A2,PA2A3, PA3A1, resp. 1,2,3 are concurrent. ...