X3949

X2260com[INVERSE(n(INCENTRAL 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) { 37, 42 }: Central Line L(37, 42) { 48, 78 }: Central Line L(48, 78) { 71, 72 }: Central Line L(71, 72) { 19, 200 }: Central Line L(19, 200) { 69, 337 }: Central Line L(69, 337) { 12, 594 }: Central Line L(12, 594) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_19 = CLAWSON POINT (0.6246, 0.4244) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_337 = ISOTOMIC CONJUGATE OF X(242) (1.0936, 0.0108) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_594 = ISOGONAL CONJUGATE OF X(593) (0.5025, 0.1672) X_3949 = com[INVERSE(n(INCENTRAL TRIANGLE))] (0.4168, 0.0651) A B C X37 X42 X48 X78 X71 X72 X19 X200 X69 X337 X12 X594 X3949 (a, b, c) = (5, 6, 7) | AB = 1

X3949 (X2260com[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 \(f(a,b,c) = bc(b + c)^{2}(b^{2} + c^{2} - a^{2})\)
Search Value (6, 9, 13): \(5.620191688581\)
▸ Incident Central Lines21 lines

{6, 976}, {8, 1953}, {9, 943}, {10, 2294}, {12, 594}, {19, 200}, {37, 42}, {48, 78}, {63, 1796}, {69, 337}, {71, 72}, {100, 1761}, {198, 480}, {201, 2197}, {219, 1807}, {306, 3610}, {319, 1959}, {518, 2260}, {1089, 1826}, {1215, 2345}, {1757, 1778}