Trilinears           1/a : 1/b : 1/c
                                    = bc : ca : ab
                                    = csc A : csc B : csc C
                                    = cos A + cos B cos C : cos B + cos C cos A : cos C + cos A cos B
                                    = sec A + sec B sec C : sec B + sec C sec A : sec C + sec A sec B
                                    = cos A + cos(B - C) : cos B + cos(C - A) : cos C + cos(A - B)
                                    = cos B cos C - cos(B - C) : cos C cos A - cos(C - A) : cos A cos B - cos(A - B)

Barycentrics    1 : 1 : 1

X(2) is the point of concurrence of the medians of ABC, situated 1/3 of the distance from each vertex to the midpoint of the opposite side. More generally, if L is any line in the plane of ABC, then the distance from X(2) to L is the average of the distances from A, B, C to L. An idealized triangular sheet balances atop a pin head located at X(2) and also balances atop any knife-edge that passes through X(2). The triangles BXC, CXA, AXB have equal areas if and only if X = X(2).

X(2) is the centroid of the set of 3 vertices, the centroid of the triangle including its interior, but not the centroid of the triangle without its interior; that centroid is X(10).

X(2) is the identity of the group of triangle centers under "barycentric multiplication" defined by

(x : y : z)*(u : v : w) = xu : yv : zw.

X(2) lies on these lines:
1,8    3,4    6,69    7,9    11,55    12,56    13,16    14,15    17,62    18,61    19,534    31,171    32,83    33,1040    34,1038    35,1479    36,535    37,75    38,244    39,76    40,946    44,89    45,88    51,262    52,1216    54,68    58,540    65,959    66,206    71,1246    72,942    74,113    77,189    80,214    85,241    92,273    94,300    95,97    98,110    99,111    101,116    102,117    103,118    104,119    106,121    107,122    108,123    109,124    112,127    128,1141    129,1298    130,1303    131,1300    133,1294    136,925    137,930    154,1503    165,516    169,1763    174,236    176,1659    178,188    187,316    196,653    201,1393    210,354    216,232    220,1170    222,651    231,1273    242,1851    243,1857    252,1166    253,1073    254,847    257,1432    261,593    265,1511    271,1034    272,284    280,318    283,580    290,327    292,334    294,949    308,702    311,570    314,941    319,1100    322,1108    330,1107    341,1219    351,804    355,944    360,1115    366,367    371,486    372,485    392,517    476,842    480,1223    489,1132    490,1131    495,956    496,1058    514,1022    523,1649    525,1640    561,716    568,1154    572,1746    573,1730    578,1092    585,1336    586,1123    588,1504    589,1505    594,1255    647,850    648,1494    650,693    664,1121    668,1015    670,1084    689,733    743,789    799,873    812,1635    846,1054    914,1442    918,1638    927,1566    954,1260    968,1738    1000,1145    1043,1834    1060,1870    1074,1785    1076,1838    1089,1224    1093,1217    1124,1378    1143,1489    1155,1836    1171,1509    1186,1207    1257,1265    1284,1403    1335,1377    1340,1349    1341,1348    1500,1574    1501,1691    1672,1681    1673,1680    1674,1679    1675,1678    1697,1706

X(2) is the {X(3),X(5)}-harmonic conjugate of X(4).

X(2) = midpoint of X(I) and X(J) for these (I,J): (3,381), (4,376), (210,354)
X(2) = reflection of X(I) in X(J) for these (I,J): (1,551), (3,549), (4,381), (5,547), (6,597), (20,376), (69,599), (148,671), (376,3), (381,5), (549,140), (551,1125), (599,141), (671,115), (903,1086), (1121,1146)

X(2) = isogonal conjugate of X(6)
X(2) = isotomic conjugate of X(2)
X(2) = cyclocevian conjugate of X(4)
X(2) = inverse-in-circumcircle of X(23)
X(2) = inverse-in-nine-point-circle of X(858)
X(2) = inverse-in-Brocard-circle of X(110)
X(2) = complement of X(2)
X(2) = anticomplement of X(2)
X(2) = anticomplementary conjugate of X(69)
X(2) = complementary conjugate of X(141)

X(2) = X(I)-Ceva conjugate of X(J) for these (I,J):
(1,192), (4,193), (6,194), (7,145), (8,144), (30,1494), (69,20), (75,8), (76,69), (83,6), (85,7), (86,1), (87,330), (95,3), (98,385), (99,523), (190,514), (264,4), (274,75), (276,264), (287,401), (290,511), (308,76), (312,329), (325,147), (333,63), (348,347), (491,487), (492,488), (523,148), (626,1502)

X(2) = cevapoint of X(I) and X(J) for these (I,J):
(1,9), (3,6), (5,216), (10,37), (32,206), (39,141), (44,214), (57,223), (114,230), (115,523), (128,231), (132,232), (140,233), (188,236)

X(2) = X(I)-cross conjugate of X(J) for these (I,J):
(1,7), (3,69), (4,253), (5,264), (6,4), (9,8), (10,75), (32,66), (37,1), (39,6), (44,80), (57,189), (75,330), (114,325), (140,95), (141,76), (142,85), (178,508), (187,67), (206,315), (214,320), (216,3), (223,329), (226,92), (230,98), (233,5), (281,280), (395,14), (396,13), (440,306), (511,290), (514,190), (523,99)

X(2) = crosspoint of X(I) and X(J) for these (I,J):
(1,87), (75,85), (76,264), (83,308), (86,274), (95,276)

X(2) = crosssum of X(I) and X(J) for these (I,J):
(1,43), (2,194), (31,41), (32,184), (42,213), (51,217), (125,826), (649,1015), (688,1084), (902,1017), (1400,1409)

X(2) = crossdifference of any two points on line X(187)X(237)

X(2) = X(I)-Hirst inverse of X(J) for these (I,J):
(1,239), (3,401), (4,297), (6,385), (21,448), (27,447), (69,325), (75,350), (98,287), (115,148), (193,230), (291,335), (298,299), (449,452)

X(2) = X(3)-line conjugate of X(237) = X(316)-line conjugate of X(187)

X(2) = X(I)-aleph conjugate of X(J) for these (I,J):
(1,1045), (2,191), (86,2), (174,1046), (333,20), (366,846)

X(2) = X(I)-beth conjugate of X(J) for these (I,J):
(2,57), (21,995) (190,2), (312,312), (333,2), (643,55), (645,2), (646,2), (648,196), (662,222)

X(2) is the unique point X (as a function of a,b,c) for which the vector-sum XA + XB + XC is the zero vector.