X1329

COMPLEMENTARY CONJUGATE OF X1

X1329 = complement of X56
< 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) { 2, 12 }: Central Line L(2, 12) { 5, 10 }: Central Line L(5, 10) { 8, 11 }: Central Line L(8, 11) { 9, 46 }: Central Line L(9, 46) { 3, 119 }: Central Line L(3, 119) { 121, 124 }: Central Line L(121, 124) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3450 = 1st SARAGOSSA POINT OF X(8) (0.6199, 0.3547) X_2 = CENTROID (0.5374, 0.2000) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_8 = NAGEL POINT (0.4694, 0.1333) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_9 = MITTENPUNKT (0.5110, 0.1615) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_119 = FEUERBACH ANTIPODE (0.3776, 0.4312) X_121 = -OF-MEDIAL-TRIANGLE (0.3061, 0.2999) X_124 = -OF-MEDIAL-TRIANGLE (0.6243, 0.0030) X_1329 = COMPLEMENTARY CONJUGATE OF X(1) (0.4903, 0.1280) A B C X3450 X2 X12 X5 X10 X8 X11 X9 X46 X3 X119 X121 X124 X1329 (a, b, c) = (5, 6, 7) | AB = 1

X1329 (COMPLEMENTARY CONJUGATE OF X1) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc[b^{2}/(a - b + c) + c^{2}/(a + b - c)]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.850493677140\)
▸ Incident Central Lines15 lines

{2, 12}, {3, 119}, {5, 10}, {8, 11}, {9, 46}, {65, 908}, {121, 124}, {140, 993}, {355, 997}, {405, 498}, {495, 1125}, {496, 519}, {499, 956}, {518, 1210}, {975, 998}

▸ Functional Relations6 relations