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) = a[b2y/v + c2z/w - a2x/u],
u = u(A,B,C) = sin 2A, v = u(B,C,A), w = u(C,A,B);
x = x(A,B,C) = u2(v2 + w2) - (v2 - w2)2, y = x(B,C,A), z = x(C,A,B)Barycentrics af(a,b,c) : bf(b,c,a) : cf(c,a,b)
X(156) = X(5)-of-tangential triangle
X(156) lies on these lines: 3,74 4,49 5,184 25,143 26,154 54,381 546,578 550,1092
X(156) is the {X(154),X(155)}-harmonic conjugate of X(26). For a list of harmonic conjugates, click More at the top of this page.
X(156) = midpoint of X(26) and X(155)