Trilinears           (b + c - a)/a : (c + a - b)/b : (a + b - c)/c
                                    = csc²(A/2) : csc²(B/2) : csc²(C/2)

Barycentrics    b + c - a : c + a - b : a + b - c

Let A'B'C' be the points in which the A-excircle meets BC, the B-excircle meets CA, and the C-excircle meets AB, respectively. The lines AA', BB', CC' concur in X(8). Another construction of A' is to start at A and trace around ABC half its perimeter, and similarly for B' and C'. Also, X(8) is the incenter of the anticomplementary triangle.

X(8) lies on these lines:
1,2    3,100    4,72    5,1389    6,594    7,65    9,346    11,1320    19,1891    20,40    21,55    29,219    31,987    33,1039    34,1041    35,993    37,941    38,986    56,404    57,1219    58,996    76,668    79,758    80,149    81,1010    101,1311    140,1483    144,516    171,1468    175,1270    176,1271    177,556    178,236    181,959    190,528    192,256    193,894    194,730    197,1603    210,312    213,981    220,294    221,651    224,914    238,983    253,307    274,1002    277,1280    278,1257    291,330    314,1264    315,760    326,1442    344,480    348,664    392,1000    405,943    406,1061    442,495    443,942    474,999    475,1063    491,1267    595,1724    599,1086    631,1385    643,1098    726,1278    860,1068    908,946    961,1460    1015,1574    1016,1083    1034,1895    1036,1183    1124,1377    1211,1834    1281,1282    1317,1388    1335,1378    1500,1573    1672,1680    1673,1681    1674,1679    1675,1679    1857,1896

X(8) is the {X(69),X(75)}-harmonic conjugate of X(7).

X(8) = reflection of X(I) in X(J) for these (I,J): (1,10), (4,355), (20,40), (100,1145), (145,1), (149,80), (192,984), (390,9), (944,2), (962,4), (1320,11), (1482,5), (1483,140)

X(8) = isogonal conjugate of X(56)
X(8) = isotomic conjugate of X(7)
X(8) = cyclocevian conjugate of X(189)
X(8) = complement of X(145)
X(8) = anticomplement of X(1)
X(8) = anticomplementary conjugate of X(8)
X(8) = X(I)-Ceva conjugate of X(J) for these (I,J): (69,329), (72,2), (312,346), (314,312), (333,9)

X(8) = X(I)-cross conjugate of X(J) for these (I,J):
(1,280), (9,2), (10,318), (11,522), (55,281), (72,78), (200,346), (210,9), (219,345), (497,7), (521,100)

X(8) = cevapoint of X(I) and X(J) for these (I,J):
(1,40), (2,144), (6,197), (9,200), (10,72), (11,522), (55,219), (175,176)

X(8) = crosspoint of X(I) and X(J) for these (I,J): (75,312), (314,333)

X(8) = crosssum of X(I) and X(J) for these (I,J):
(1,978), (31,604), (57,1423), (667,1015), (1042,1410), (1400,1402)

X(8) = crossdifference of any two points on line X(649)X(854)
X(8) = X(1)-aleph conjugate of X(1050)
X(8) = X(I)-beth conjugate of X(J) for these (I,J): (8,1), (341,341), (643,3), (668,8), (1043,8)