X3792

X190com[INVERSE(nT(bc, c²))]

< 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, 674 }: Central Line L(1, 674) { 238, 511 }: Central Line L(238, 511) { 320, 758 }: Central Line L(320, 758) { 788, 1491 }: Central Line L(788, 1491) { 36, 2245 }: Central Line L(36, 2245) { 984, 1469 }: Central Line L(984, 1469) 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_674 = CROSSDIFFERENCE OF X(6) AND X(514) (0.2078, -0.2856) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_320 = ISOTOMIC CONJUGATE OF X(80) (-2.6735, -3.5993) X_758 = EVEN (1, 3) INFINITY POINT (0.1821, -0.2671) X_788 = ODD (- 3, 0) INFINITY POINT (1.0251, -0.1264) X_1491 = CROSSDIFFERENCE OF X(1) AND X(32) (25.5000, -10.6145) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_2245 = -ISOCONJUGATE OF X(759) (1.8169, 2.2770) X_984 = MIDPOINT OF X(8) AND X(192) (0.5421, 0.1984) X_1469 = -BETH CONJUGATE OF X(984) (0.6171, 0.3088) X_3792 = com[INVERSE(nT(bc, c2))] (3.2952, 4.2458) A B C X1 X674 X238 X511 X320 X758 X788 X1491 X36 X2245 X984 X1469 X3792 (a, b, c) = (5, 6, 7) | AB = 1

X3792 (X190com[INVERSE(nT(bc, c²))]) 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 \(f(a,b,c) = a^{2}(a^{2} - b^{2} - c^{2} + bc)(b^{2} + c^{2} + bc)\)
Search Value (6, 9, 13): \(-13.900044497150\)
▸ Incident Central Lines11 lines

{1, 674}, {31, 2979}, {36, 2245}, {238, 511}, {320, 758}, {748, 3060}, {788, 1491}, {984, 1469}, {1216, 3072}, {1944, 2607}, {2175, 3098}