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) = (1 + cos 2B + cos 2C) sin 3A csc 2A
Barycentrics (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)Let A'B'C' be the orthic triangle of triangle ABC. Let A_{B} be the reflection of A in C', and define A_{C}, B_{C}, B_{A}, C_{A}, C_{B} functionally. Then the nine-point circles of the triangles
AA_{B}A_{C}, BB_{C}B_{A}, CC_{A}C_{B}, concur in X(1986). (Antreas Hatzipolakis, Hyacinthos 7868, 9/12/03; coordinates by Barry Wolk, Hyacinthos 7876, 9/13/03)
X(1986) lies on these lines:
9,94 6,74 24,110 25,399 113,403 125,389 186,323 542,1843 648,1300 1844,1845X(1986) = reflection of X(I) in X(J) for these (I,J): (4,1112), (74,974), (125,389)
X(1986) = X(4)-Ceva conjugate of X(403)
X(1986) = crosspoint of X(4) and X(186)
X(1986) = crosssum of X(3) and X(265)