X3954

X2295com[INVERSE(n(INCENTRAL TRIANGLE))]

X3954 = complement of X17141
< 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, 6 }: Incenter–Symmedian Line { 38, 39 }: Central Line L(38, 39) { 76, 321 }: Central Line L(76, 321) { 274, 335 }: Central Line L(274, 335) { 10, 762 }: Central Line L(10, 762) { 100, 755 }: Central Line L(100, 755) 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_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5168, 0.1843) X_335 = ISOTOMIC CONJUGATE OF X(239) (1.0387, 0.0318) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_762 = TRILINEAR CUBE OF X(37) (0.5240, 0.1822) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_755 = EVEN (0, 4) CIRCUMCIRCLE POINT (0.9524, -0.1340) X_3954 = com[INVERSE(n(INCENTRAL TRIANGLE))] (0.5276, 0.1812) A B C X1 X6 X38 X39 X76 X321 X274 X335 X10 X762 X100 X755 X3954 (a, b, c) = (5, 6, 7) | AB = 1

X3954 (X2295com[INVERSE(n(INCENTRAL 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 \(f(a,b,c) = a(b + c)(b^{2} + c^{2})\)
Search Value (6, 9, 13): \(2.864614399212\)
▸ Incident Central Lines19 lines

{1, 6}, {8, 3735}, {10, 762}, {32, 976}, {38, 39}, {76, 321}, {100, 755}, {141, 1930}, {228, 2156}, {257, 668}, {274, 335}, {519, 3727}, {758, 2295}, {1125, 3726}, {1500, 2292}, {1575, 3670}, {1655, 2895}, {1843, 3688}, {2238, 3678}

▸ Functional Relations1 relation

  • X3954 = complement of X17141