X3727

X2295com(INCENTRAL TRIANGLE)

X3727 = isogonal conjugate of isotomic conjugate of X21442
< 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, 32 }: Central Line L(1, 32) { 257, 350 }: Central Line L(257, 350) { 37, 1953 }: Central Line L(37, 1953) { 517, 2295 }: Central Line L(517, 2295) { 960, 2238 }: Central Line L(960, 2238) { 55, 3148 }: Central Line L(55, 3148) 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_32 = 3rd POWER POINT (0.6400, 0.3332) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_350 = -HIRST INVERSE OF X(75) (-3.5227, -3.1370) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_1953 = BICENTRIC SUM OF PU(21) (0.5856, 0.2841) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_2295 = -ISOCONJUGATE OF X(1178) (0.5682, 0.2347) X_960 = INTERSECTION OF LINES X(1)X(6) AND X(5)X(10) (0.5041, 0.1533) X_2238 = -ISOCONJUGATE OF X(741) (2.2505, 2.0410) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_3148 = -CEVA CONJUGATE OF X(6) (0.5769, 0.3032) X_3727 = com(INCENTRAL TRIANGLE) (0.5524, 0.2055) A B C X1 X32 X257 X350 X37 X1953 X517 X2295 X960 X2238 X55 X3148 X3727 (a, b, c) = (5, 6, 7) | AB = 1

X3727 (X2295com(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 \(f(a,b,c) = a(2abc + b^{3} + c^{3})\)
Search Value (6, 9, 13): \(2.255232790652\)
▸ Incident Central Lines12 lines

{1, 32}, {37, 1953}, {55, 3148}, {257, 350}, {517, 2295}, {762, 3626}, {960, 2238}, {986, 2275}, {1100, 2650}, {1107, 2170}, {1125, 3125}, {2276, 3061}

▸ Functional Relations1 relation

  • X3727 = isogonal conjugate of isotomic conjugate of X21442