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 1/(1 + sin A) : 1/(1 + sin B) : 1/(1 + sin C)
Barycentrics (sin A)/(1 + sin A) : (sin B)/(1 + sin B) : (sin C)/(1 + sin C)Let D and E be the congruent circles each tangent to the other and to line BC, with D also tangent to line AB and E also tangent to one CA, meeting in a point A' lying outside triangle ABC. Define B' and C' cyclically. Then A'B'C' is perspective to ABC, and the perspector is X(1123). See
Ivan Paasche, Aufgabe P 933, Praxis der Mathematik 1 (1990), page 40.
X(1123) lies on these lines: 2,586 37,158 57,482
X(1123) = isogonal conjugate of X(1124)
X(1123) = isotomic conjugate of X(1267)