X3884

X3628com[INVERSE(n(4th EULER TRIANGLE))]

X3884 = X10-of-X1-Brocard 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) { 10, 11 }: Central Line L(10, 11) { 1, 21 }: Central Line L(1, 21) { 35, 214 }: Central Line L(35, 214) { 65, 551 }: Central Line L(65, 551) { 140, 517 }: Central Line L(140, 517) { 519, 960 }: Central Line L(519, 960) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_1 = INCENTER (0.5714, 0.2333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_214 = -CEVA CONJUGATE OF X(44) (0.3571, 0.3499) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_551 = MIDPOINT OF X(1) AND X(2) (0.5544, 0.2166) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_960 = INTERSECTION OF LINES X(1)X(6) AND X(5)X(10) (0.5041, 0.1533) X_3884 = com[INVERSE(n(4th EULER TRIANGLE))] (0.5296, 0.1783) A B C X10 X11 X1 X21 X35 X214 X65 X551 X140 X517 X519 X960 X3884 (a, b, c) = (5, 6, 7) | AB = 1

X3884 (X3628com[INVERSE(n(4th EULER TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(b^{3} + c^{3} - a^{2}b - a^{2}c + 4abc)\)
Search Value (6, 9, 13): \(2.974894819707\)
▸ Incident Central Lines19 lines

{1, 21}, {10, 11}, {35, 214}, {65, 551}, {72, 3244}, {140, 517}, {210, 3625}, {405, 2098}, {518, 3635}, {519, 960}, {942, 3636}, {997, 1697}, {1000, 2551}, {1001, 1482}, {1149, 3670}, {1385, 2800}, {2170, 3294}, {3230, 3727}, {3633, 3681}

▸ Functional Relations1 relation