X3959

X2176com(ORTHIC TRIANGLE)

X3959 = polar conjugate of isogonal conjugate of X23526
< 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) { 6, 19 }: Central Line L(6, 19) { 75, 257 }: Central Line L(75, 257) { 85, 1086 }: Central Line L(85, 1086) { 1, 1929 }: Central Line L(1, 1929) { 986, 1107 }: Central Line L(986, 1107) { 517, 2176 }: Central Line L(517, 2176) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_19 = CLAWSON POINT (0.6246, 0.4244) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7687, 0.1000) X_1 = INCENTER (0.5714, 0.2333) X_1929 = ISOGONAL CONJUGATE OF X(1757) (0.9903, -0.0202) X_986 = INTERSECTION OF LINES X(1)X(3) AND X(8)X(38) (0.5588, 0.2101) X_1107 = CROSSPOINT OF X(1) AND X(274) (0.5495, 0.2072) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_2176 = -ISOCONJUGATE OF X(87) (0.6513, 0.3282) X_3959 = com(ORTHIC TRIANGLE) (0.5927, 0.2204) A B C X6 X19 X75 X257 X85 X1086 X1 X1929 X986 X1107 X517 X2176 X3959 (a, b, c) = (5, 6, 7) | AB = 1

X3959 (X2176com(ORTHIC 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 \(f(a,b,c) = a(b^{3} + c^{3} - b^{2}c - bc^{2} + abc)\)
Search Value (6, 9, 13): \(1.563675779923\)
▸ Incident Central Lines18 lines

{1, 1929}, {2, 3727}, {6, 19}, {8, 3721}, {10, 3735}, {37, 3208}, {75, 257}, {85, 1086}, {145, 3726}, {517, 2176}, {982, 2319}, {986, 1107}, {1575, 3061}, {1738, 3094}, {1953, 2277}, {2170, 2275}, {2643, 3764}, {3057, 3290}

▸ Functional Relations1 relation

  • X3959 = polar conjugate of isogonal conjugate of X23526