X1870

ZOSMA TRANSFORM OF X484

X1870 = homothetic center of circumorthic triangle and anti-tangential midarc triangle
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 1, 4 }: Incenter–Orthocenter Line { 24, 56 }: Central Line L(24, 56) { 28, 60 }: Central Line L(28, 60) { 54, 65 }: Central Line L(54, 65) { 36, 186 }: Central Line L(36, 186) { 11, 403 }: Central Line L(11, 403) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1807 = INVERSE MIMOSA TRANSFORM OF X(484) (0.8312, -0.0318) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6627, 0.5278) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_60 = ISOGONAL CONJUGATE OF X(12) (0.5790, 0.2258) X_54 = KOSNITA POINT (0.5880, 0.2176) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_186 = INVERSE-IN-CIRCUMCIRCLE OF X(4) (0.7957, 0.8758) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_403 = OF THE ORTHIC TRIANGLE (0.7040, 0.6358) X_1870 = ZOSMA TRANSFORM OF X(484) (0.6984, 0.7387) A B C X1807 X1 X4 X24 X56 X28 X60 X54 X65 X36 X186 X11 X403 X1870 (a, b, c) = (5, 6, 7) | AB = 1

X1870 (ZOSMA TRANSFORM OF X484) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: (y + z) sec A : (z + x) sec B : (x + y) sec C,\(x : y : z\) = X484
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X484
Search Value (6, 9, 13): \(0.658900400303\)
▸ Alternate Coordinates3 forms

  • Trilinears: \(2 - \sec A : 2 - \sec B : 2 - \sec C\)

  • Trilinears: \((a^{2} - b^{2} + b c - c^{2})/(a^{2} - b^{2} - c^{2}) : :\)

  • Trilinears: \((2 - 2 \cos A + \cos B + \cos C) \sec A : :\)

▸ Incident Central Lines44 lines

{1, 4}, {2, 1060}, {3, 1398}, {7, 1061}, {8, 475}, {11, 403}, {12, 1594}, {19, 1449}, {20, 1062}, {24, 56}, {25, 999}, {28, 60}, {36, 186}, {54, 65}, {55, 378}, {59, 517}, {77, 1119}, {104, 1455}, {108, 953}, {109, 1735}, {208, 1420}, {221, 1181}, {232, 1015}, {235, 496}, {242, 514}, {273, 1442}, {354, 1905}, {376, 1040}, {389, 1425}, {427, 495}, {451, 1125}, {459, 614}, {519, 1861}, {631, 1038}, {651, 912}, {982, 1395}, {1000, 1041}, {1006, 1214}, {1100, 1172}, {1318, 1878}, {1385, 1426}, {1718, 1737}, {1725, 1776}, {1831, 1844}

▸ Functional Relations5 relations