zltnv
Posts:
5
Registered:
7/24/07


triangle center
Posted:
Jul 24, 2007 7:16 PM


While working on a problem not exactly in plane geometry, I seem to have established the statement below. I wonder if any one has seen it before or can recognize it as equivalent to a known fact. It may be related to the Miquel point theorem, which came out in a related problem.
On the sides (and continuations) of triangle ABC take points Ac, Bc, ..., Ab :
on AB : Ac, Bc, s.t. A>Ac = B>Bc; on BC : Ba, Ca, s.t. B>Ba = C>Ca; on CA : Cb, Ab, s.t. C>Cb = A>Ab;
A>Ac is the vector (_directed_ segment) from A to Ac.
Let tA, tB, tC be the tangents to the circumcircles of AAbA, BBaBc, CCbCa at A, B, C.
Then tA, tB, tC are concurrent or all parallel.
Dimiter Zlatanov

