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) = (csc A)/[(3 - cot B cot C)(3 - cot^{2}A)]
Barycentrics (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)
Let N denote the nine-point center, X(5). Let N_{A} = N-of-triangle NBC, and define N_{B} and N_{C} cyclically. Triangle N_{A}N_{B}N_{C} is perspective to ABC, and X(1487) is the perspector. X(1487) is the cevapoint of the Napoleon points, X(17) and X(18). (Coordinates found by Paul Yiu.)
The construction just given for X(1487) shows that it is a solution X of the "four-triangle problem" posed in
C. Kimberling, "Triangle centers as functions," Rocky Mountain Journal of Mathematics 23 (1993) 1269-1286. See Section 5; a complete solution to the problem remains to be found.
X(1487) lies on these lines: 4,252 5,1173 140,930
X(1487) = isogonal conjugate of X(1493)
X(1487) = cevapoint of X(17) and X(18)
X(1487) = X(523)-cross conjugate of X(930)