X3995

X756com[INVERSE(n(INCENTRAL TRIANGLE))]

X3995 = homothetic center of anticomplementary triangle and inverse of n(Medial)*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) { 2, 37 }: Central Line L(2, 37) { 72, 145 }: Central Line L(72, 145) { 81, 190 }: Central Line L(81, 190) { 86, 1255 }: Central Line L(86, 1255) { 740, 756 }: Central Line L(740, 756) { 8, 2901 }: Central Line L(8, 2901) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_1255 = ISOGONAL CONJUGATE OF X(1100) (0.5639, 0.2247) X_740 = EVEN (- 1, 1) INFINITY POINT (0.9745, 0.5915) X_756 = CROSSPOINT OF X(10) AND X(37) (0.5409, 0.1988) X_8 = NAGEL POINT (0.4694, 0.1333) X_2901 = ORTHIC-ISOGONAL CONJUGATE OF X(10) (0.8536, 0.4818) X_3995 = com[INVERSE(n(INCENTRAL TRIANGLE))] (0.5957, 0.2478) A B C X2 X37 X72 X145 X81 X190 X86 X1255 X740 X756 X8 X2901 X3995 (a, b, c) = (5, 6, 7) | AB = 1

X3995 (X756com[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 \(f(a,b,c) = (b + c)(a^{2} + ab + ac - bc)\)
Search Value (6, 9, 13): \(0.974934496091\)
▸ Incident Central Lines14 lines

{1, 3159}, {2, 37}, {8, 2901}, {9, 3187}, {72, 145}, {81, 190}, {86, 1255}, {239, 3294}, {726, 3720}, {740, 756}, {1089, 3743}, {1215, 1962}, {1655, 2895}, {1999, 3219}

▸ Functional Relations2 relations

  • X3995 = complement of X4359

  • X3995 = homothetic center of anticomplementary triangle and inverse of n(Medial)*n(Incentral) triangle