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 (cos B/2 + cos C/2) csc A : (cos C/2 + cos A/2) csc B : (cos A/2 + cos B/2) csc C
Barycentrics cos B/2 + cos C/2 : cos C/2 + cos A/2 : cos A/2 + cos B/2Let A',B',C' be the first points of intersection of the angle bisectors of ABC with its incircle. Let A",B",C" be the midpoints of segments BC,CA,AB, respectively. The lines A'A",B'B",C'C" concur in X(178).
Clark Kimberling, Problem 804, Nieuw Archikef voor Wiskunde 6 (1988) 170.
X(178) lies on these lines: 2,188 8,236
X(178) = complement of X(188)
X(178) = crosspoint of X(2) and X(508)