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) = a3 + a(bc - b2 - c2) - bc(b + c)
Barycentrics af(a,b,c) : bf(b,c,a) : cf(c,a,b)The term "AC-incircle" is introduced for "anticomplement of the incircle" by Peter Moses (Dec. 2, 2004). Thus, the AC-incircle is the incircle of the anticomplementary triangle; the circle has center X(8) and radius 2r. The exsimilicenter of the circumcircle and AC-incircle is X(100), their touchpoint, and the anticomplement of X(11).
X(2975) lies on these lines:
1,21 2,12 3,8 9,604 10,36 20,2894 28,92 35,519 48,2287 54,72 55,145 75,1444 78,947 105,330 110,1098 144,1001 172,1107 198,391 229,409 238,1201 329,405 333,1610 348,934 411,515 518,2330 593,2363 596,759 668,1078 672,2329 908,1125 943,2320 950,1005 960,1319 962,1012 966,2178 995,1724 1457,1935 1470,1788 1478,2476 1761,1953 2475,2886X(2975) = anticomplement of X(12)
X(2975) = X(I)-Ceva conjugate of X(J) for these I,J: 59,100 261,2
X(2975) = crosssum of X(512) and X(2170)