X3755

X6com[INVERSE(n(HEXYL 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, 37 }: Central Line L(10, 37) { 1, 142 }: Central Line L(1, 142) { 42, 226 }: Central Line L(42, 226) { 40, 387 }: Central Line L(40, 387) { 6, 516 }: Central Line L(6, 516) { 519, 599 }: Central Line L(519, 599) 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_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_1 = INCENTER (0.5714, 0.2333) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_40 = BEVAN POINT (0.4286, -0.0292) X_387 = INTERSECTION OF LINES X(1,2) AND X(4,6) (0.5994, 0.2607) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_599 = ISOTOMIC CONJUGATE OF X(598) (0.4748, 0.1327) X_3755 = com[INVERSE(n(HEXYL TRIANGLE))] (0.5911, 0.2466) A B C X10 X37 X1 X142 X42 X226 X40 X387 X6 X516 X519 X599 X3755 (a, b, c) = (5, 6, 7) | AB = 1

X3755 (X6com[INVERSE(n(HEXYL 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 \(f(a,b,c) = (b + c)(3a^{2} + b^{2} + c^{2} - 2bc)\)
Search Value (6, 9, 13): \(1.343578558799\)
▸ Linear Combinations1 combination
▸ Incident Central Lines17 lines

{1, 142}, {4, 2331}, {6, 516}, {10, 37}, {40, 387}, {42, 226}, {43, 3452}, {65, 1439}, {386, 946}, {497, 2999}, {515, 990}, {519, 599}, {528, 1386}, {908, 3240}, {1001, 3008}, {1886, 2266}, {2177, 3011}