Trilinears bc(b + c) : ca(c + a) : ab(a + b)
Barycentrics b + c : c + a : a + b
The Spieker circle is the incircle of the medial triangle; its center, X(10), is the centroid of the perimeter of ABC.
X(10) lies on these lines:
1,2 3,197 4,9 5,517 6,1377 11,121 12,65 20,165 21,35 28,1891 29,1794 31,964 33,406 34,475 36,404 37,594 38,596 39,730 44,752 46,63 55,405 56,474 57,388 58,171 69,969 75,76 81,1224 82,83 86,319 87,979 92,1838 98,101 106,1222 116,120 117,123 119,124 140,214 141,142 150,1282 153,1768 158,318 182,1678 190,671 191,267 201,225 219,965 227,1214 235,1902 255,1771 257,1581 261,1326 274,291 307,1254 321,756 348,1323 391,1743 407,1867 427,1829 429,1824 480,954 485,1686 486,1685 497,1697 514,764 535,1155 537,1086 626,760 631,944 632,1483 750,1150 774,1736 775,801 846,1247 894,1046 908,994 962,1695 1018,1334 1074,1735 1146,1212 1482,1656 1587,1703 1588,1702 1762,1782 1828,1883 1900,1904
X(10) is the {X(1),X(2)}-harmonic conjugate of X(1125).
X(10) = midpoint of X(I) and X(J) for these (I,J): (1,8), (3,355), (4,40), (65,72), (80,100)
X(10) = reflection of X(I) in X(J) for these (I,J): (1,1125), (551,2), (946,5), (1385,140)
X(10) = isogonal conjugate of X(58)
X(10) = isotomic conjugate of X(86)
X(10) = inverse-in-circumcircle of X(1324)
X(10) = complement of X(1)
X(10) = anticomplement of X(1125)
X(10) = complementary conjugate of X(10)
X(10) = X(I)-Ceva conjugate of X(J) for these (I,J):
(2,37), (8,72), (75,321), (80,519), (100,522), (313,306)
X(10) = cevapoint of X(I) and X(J) for these (I,J): (1,191), (6,199), (12,201), (37,210), (42,71), (65,227)
X(10) = X(I)-cross conjugate of X(J) for these (I,J): (37,226), (71,306), (191,502), (201,72)
X(10) = crosspoint of X(I) and X(J) for these (I,J): (2,75), (8,318)
X(10) = crosssum of X(I) and X(J) for these (I,J): (6,31), (56,603)
X(10) = crossdifference of any two points on line X(649)X(834)
X(10) = X(I)-beth conjugate of X(J) for these (I,J): (8,10), (10,65), (100,73), (318,225), (643,35), (668,349)
, select the center name from the list and, then, click on the vertices A, B and C successively.