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 1/(1 - sec A) : 1/(1 - sec B) : 1/(1 - sec C)
= cos A csc2(A/2) : cos B csc2(B/2) : cos C csc2(C/2)
= (b + c - a)(b2 + c2 - a2) : (c + a - b)(c2 + a2 - b2) : (a + b - c)(a2 + b2 - c2)Barycentrics a/(1 - sec A) : b/(1 - sec B) : c/(1 - sec C)
X(78) lies on these lines:
1,2 3,63 4,908 9,21 20,329 29,33 37,965 38,988 40,100 46,758 55,960 56,480 57,404 69,73 101,205 207,653 210,958 212,283 220,949 226,377 271,394 273,322 280,282 345,1040 392,1057 474,942 517,945 644,728 999,1059X(78) = isogonal conjugate of X(34)
X(78) = isotomic conjugate of X(273)
X(78) = X(I)-Ceva conjugate of X(J) for these (I,J): (69,63), (312,9), (332,345)
X(78) = X(I)-cross conjugate of X(J) for these (I,J): (3,271), (72,8), (212,9), (219,63)
X(78) = crosspoint of X(69) and X(345)
X(78) = crosssum of X(I) and X(J) for these (I,J): (25,608), (56,1406), (604,1395), (1042,1426)
X(78) = X(I)-beth conjugate of X(J) for these (I,J): (78,3), (643,40), (1043,1)