X3732

X3022com(EXCENTRAL 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) { 85, 169 }: Central Line L(85, 169) { 144, 153 }: Central Line L(144, 153) { 101, 514 }: Central Line L(101, 514) { 190, 646 }: Central Line L(190, 646) { 150, 1146 }: Central Line L(150, 1146) { 651, 653 }: Central Line L(651, 653) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) X_144 = ANTICOMPLEMENT OF X(7) (0.4317, 0.0461) X_153 = REFLECTION OF X(20) IN X(100) (-0.1020, 1.1248) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_646 = BARYCENTRIC MULTIPLIER FOR YFF PARABOLA (-0.0898, 0.2051) X_150 = REFLECTION OF X(20) IN X(103) (1.1837, -0.4499) X_1146 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(8)}} (0.6866, 0.0428) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_653 = TRILINEAR POLE OF LINE X(1)X(4) (0.5097, 0.6030) X_3732 = com(EXCENTRAL TRIANGLE) (0.1895, 0.5356) A B C X85 X169 X144 X153 X101 X514 X190 X646 X150 X1146 X651 X653 X3732 (a, b, c) = (5, 6, 7) | AB = 1

X3732 (X3022com(EXCENTRAL 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 \(f(a,b,c) = (a^{2} + b^{2} + c^{2} - 2bc)/(b - c)\)
Search Value (6, 9, 13): \(1.907398619175\)
▸ Incident Central Lines12 lines

{2, 1565}, {3, 3177}, {85, 169}, {100, 1292}, {101, 514}, {144, 153}, {150, 1146}, {190, 646}, {218, 3212}, {544, 1121}, {651, 653}, {673, 1111}