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 2A cos(B - C) : cos 2B cos(C - A) : cos 2C cos(A - B)
= f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = sec A (sec 2B + sec 2C)Barycentrics tan A (sec 2B + sec 2C) : tan B (sec 2C + sec 2A) : tan C (sec 2A + sec 2B)
X(52) lies on these lines:
3,6 4,68 5,51 25,155 26,184 30,185 49,195 113,135 114,211 128,134 129,139X(52) is the {X(5),X(143)}-harmonic conjugate of X(51).
X(52) = reflection of X(I) in X(J) for these (I,J): (3,389), (5,143), (113,1112), (1209,973)
X(52) = isogonal conjugate of X(96)
X(52) = anticomplement of X(1216)
X(52) = inverse-in-Brocard-circle of X(569)
X(52) = X(I)-Ceva conjugate of X(J) for these (I,J): (4,5), (317,467), (324,216)
X(52) = crosspoint of X(4) and X(24)
X(52) = crosssum of X(3) and X(68)