X3750

X846com[n(MEDIAL)*n(INCENTRAL)]

< 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, 3 }: OI Line (Incenter–Circumcenter Line) { 42, 238 }: Central Line L(42, 238) { 333, 519 }: Central Line L(333, 519) { 81, 902 }: Central Line L(81, 902) { 43, 1001 }: Central Line L(43, 1001) { 518, 846 }: Central Line L(518, 846) 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_3 = CIRCUMCENTER (0.5000, 0.1021) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_902 = CROSSPOINT OF X(6) AND X(106) (1.2500, 1.2247) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_1001 = MIDPOINT OF X(1) AND X(9) (0.5412, 0.1974) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_846 = 4th SHARYGIN POINT (0.5437, 0.1969) X_3750 = com[n(MEDIAL)*n(INCENTRAL)] (0.5660, 0.2234) A B C X1 X3 X42 X238 X333 X519 X81 X902 X43 X1001 X518 X846 X3750 (a, b, c) = (5, 6, 7) | AB = 1

X3750 (X846com[n(MEDIAL)*n(INCENTRAL)]) 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 \(f(a,b,c) = a(a^{2} - 2ab - 2ac - bc)\)
Search Value (6, 9, 13): \(1.877688615611\)
▸ Incident Central Lines12 lines

{1, 3}, {2, 2177}, {42, 238}, {43, 1001}, {81, 902}, {99, 2668}, {256, 2346}, {333, 519}, {518, 846}, {748, 3240}, {941, 983}, {968, 984}