X3794

X2com[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, 21 }: Central Line L(1, 21) { 2, 51 }: Central Line L(2, 51) { 210, 333 }: Central Line L(210, 333) { 86, 1431 }: Central Line L(86, 1431) { 29, 1828 }: Central Line L(29, 1828) { 404, 1730 }: Central Line L(404, 1730) 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_21 = SCHIFFLER POINT (0.5287, 0.1771) X_2 = CENTROID (0.5374, 0.2000) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_1431 = -BETH CONJUGATE OF X(256) (0.6270, 0.3250) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_1828 = ZOSMA TRANSFORM OF X(8) (0.6327, 0.4332) X_404 = {X(2),X(3)}-HARMONIC CONJUGATE OF X(21) (0.5538, 0.2429) X_1730 = MIMOSA TRANSFORM OF X(86) (0.6546, 0.4410) X_3794 = com[INVERSE(nT(-bc, c2))] (0.5037, 0.1442) A B C X1 X21 X2 X51 X210 X333 X86 X1431 X29 X1828 X404 X1730 X3794 (a, b, c) = (5, 6, 7) | AB = 1

X3794 (X2com[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 \(f(a,b,c) = a(a + b)(a + c)(b + c - a)(b^{2} + c^{2} - bc)\)
Search Value (6, 9, 13): \(3.545673544448\)
▸ Incident Central Lines10 lines

{1, 21}, {2, 51}, {29, 1828}, {86, 1431}, {210, 333}, {404, 1730}, {1010, 3753}, {1330, 2478}, {1403, 3286}, {3056, 3705}