Interactive Applet |
You can move the points A, B and C (click on the point and drag it).
Press the keys “+” and “−” to zoom in or zoom out the visualization window and use the arrow keys to translate it.
You can also construct all centers related with this one (as described in ETC) using the “Run Macro Tool”. To do this, click on the icon , select the center name from the list and, then, click on the vertices A, B and C successively.
Information from Kimberling's Encyclopedia of Triangle Centers |
Trilinears f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = cos B/2 + cos C/2 - cos A/2
Trilinears tan(A/2) + sec(A/2) : tan(B/2) + sec(B/2) : tan(C/2) + sec(C/2) (M. Iliev, 4/12/07)
Barycentrics g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)
Let P(B)Q(C) be an isoscelizer: let P(B) on sideline AC and Q(C) on AB be equidistant from A, so that AP(B)Q(C) is an isosceles triangle. Line P(B)-to-Q(C), P(C)-to-Q(A), P(A)-to-Q(B) concur in X(173). (P. Yff, unpublished notes, 1989)
The intouch triangle of the intouch triangle of triangle ABC is perspective to triangle ABC, and X(173) is the perspector. (Eric Danneels, Hyacinthos 7892, 9/13/03)
Also, X(173) = X(1486)-of-the-intouch-triangle. (Darij Grinberg; see notes at X(1485) and X(1486).)
Congruent Isoscelizers Point.
X(173) lies on these lines: 1,168 9,177 57,174 164,504 180,483 503,844 505,1130
X(173) = isogonal conjugate of X(258)
X(173) = X(174)-Ceva conjugate of X(1)X(173) = X(I)-aleph conjugate of X(J) for these (I,J):
(1,503), (2,504), (174,173), (188,845), (366,164), (507,1), (508,362), (509,361)