X3874

X140com[INVERSE(n(3rd EULER TRIANGLE))]

X3874 = complement of X5904
< 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, 21 }: Central Line L(1, 21) { 10, 141 }: Central Line L(10, 141) { 56, 214 }: Central Line L(56, 214) { 72, 354 }: Central Line L(72, 354) { 65, 519 }: Central Line L(65, 519) { 517, 550 }: Central Line L(517, 550) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_214 = -CEVA CONJUGATE OF X(44) (0.3571, 0.3499) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_354 = WEILL POINT (0.5823, 0.2533) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_550 = MIDPOINT OF X(3) AND X(20) (0.4439, -0.0448) X_3874 = com[INVERSE(n(3rd EULER TRIANGLE))] (0.6551, 0.3433) A B C X1 X21 X10 X141 X56 X214 X72 X354 X65 X519 X517 X550 X3874 (a, b, c) = (5, 6, 7) | AB = 1

X3874 (X140com[INVERSE(n(3rd 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 \(f(a,b,c) = a(b^{3} + c^{3} - a^{2}b - a^{2}c - 2abc)\)
Search Value (6, 9, 13): \(-0.878864111042\)
▸ Linear Combinations1 combination
▸ Incident Central Lines35 lines

{1, 21}, {2, 3678}, {4, 2801}, {7, 2894}, {8, 2891}, {10, 141}, {35, 3218}, {40, 3243}, {42, 3670}, {56, 214}, {65, 519}, {72, 354}, {78, 3338}, {92, 1844}, {100, 3336}, {145, 2802}, {210, 3634}, {213, 3726}, {244, 3216}, {295, 2809}, {386, 982}, {392, 3636}, {404, 3337}, {516, 1071}, {517, 550}, {551, 960}, {726, 2901}, {912, 946}, {997, 3333}, {1482, 2800}, {1698, 3681}, {1739, 3214}, {1759, 2280}, {3057, 3635}, {3626, 3753}

▸ Functional Relations2 relations

  • X3874 = complement of X5904

  • X3874 = X13419-of-excentral-triangle