X3935

X1155com[INVERSE(n(INTOUCH TRIANGLE))]

X3935 = inverse-in-circumconic-centered-at-X1 of X2
< 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) incircle: Incircle of △ABC { 1, 2 }: Nagel Line { 100, 518 }: Central Line L(100, 518) { 44, 765 }: Central Line L(44, 765) { 149, 908 }: Central Line L(149, 908) { 72, 1005 }: Central Line L(72, 1005) { 88, 1280 }: Central Line L(88, 1280) 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_2 = CENTROID (0.5374, 0.2000) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_765 = CEVAPOINT OF X(1) AND X(100) (0.4286, 0.3110) X_149 = REFLECTION OF X(20) IN X(104) (1.3265, -0.3333) X_908 = POINT ACUBENS (-0.8367, -1.7996) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_1005 = INTERCEPT OF EULER LINE AND LINE X(9)X(100) (0.5199, 0.1541) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_1280 = ISOGONAL CONJUGATE OF X(1279) (1.1600, 0.1306) X_3935 = com[INVERSE(n(INTOUCH TRIANGLE))] (-3.0000, -3.2660) A B C X1 X2 X100 X518 X44 X765 X149 X908 X72 X1005 X88 X1280 X3935 (a, b, c) = (5, 6, 7) | AB = 1

X3935 (X1155com[INVERSE(n(INTOUCH 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 \(f(a,b,c) = a(a^{2} + b^{2} + c^{2} - 2ab - 2ac + bc)\)
Search Value (6, 9, 13): \(17.221677274363\)
▸ Incident Central Lines27 lines

{1, 2}, {44, 765}, {55, 1776}, {63, 3158}, {72, 1005}, {88, 1280}, {100, 518}, {144, 3174}, {149, 908}, {210, 1621}, {238, 3722}, {329, 2900}, {404, 3555}, {522, 4724}, {678, 896}, {740, 1109}, {756, 3750}, {758, 3245}, {902, 1757}, {984, 2177}, {1001, 3711}, {1071, 3579}, {2246, 3684}, {3189, 3436}, {3243, 3306}, {3678, 3746}, {3740, 3748}

▸ Functional Relations2 relations

  • X3935 = inverse-in-circumconic-centered-at-X1 of X2

  • X3935 = endo-homothetic center of X2- and X3-Ehrmann triangles; the homothetic center is X15139