X3780

X3721com[T(-bc, b²)]

< 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) { 6, 8 }: Central Line L(6, 8) { 213, 519 }: Central Line L(213, 519) { 42, 1107 }: Central Line L(42, 1107) { 44, 1334 }: Central Line L(44, 1334) { 1, 1573 }: Central Line L(1, 1573) { 992, 1100 }: Central Line L(992, 1100) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_8 = NAGEL POINT (0.4694, 0.1333) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_1107 = CROSSPOINT OF X(1) AND X(274) (0.5495, 0.2072) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_1334 = POINT ALYA (0.5324, 0.1760) X_1 = INCENTER (0.5714, 0.2333) X_1573 = INSIMILICENTER OF SPIEKER AND MOSES CIRCLES (0.5399, 0.1993) X_992 = INTERSECTION OF LINES X(2)X(6) AND X(9)X(39) (0.2678, -0.0897) X_1100 = COMPLEMENT OF X(319) (0.5787, 0.2419) X_3780 = com[T(-bc, b2)] (0.6618, 0.3306) A B C X6 X8 X213 X519 X42 X1107 X44 X1334 X1 X1573 X992 X1100 X3780 (a, b, c) = (5, 6, 7) | AB = 1

X3780 (X3721com[T(-bc, b²)]) 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 \(f(a,b,c) = a(a^{2}b + a^{2}c + 2abc - b^{2}c - bc^{2})\)
Search Value (6, 9, 13): \(-0.346992227474\)
▸ Incident Central Lines22 lines

{1, 1573}, {6, 8}, {37, 3691}, {39, 3293}, {42, 1107}, {43, 2275}, {44, 1334}, {72, 3727}, {145, 2176}, {172, 3684}, {213, 519}, {239, 1909}, {518, 3721}, {956, 2271}, {992, 1100}, {1015, 3216}, {1230, 3187}, {1475, 1575}, {1724, 2241}, {1743, 3208}, {3230, 3244}, {3555, 3726}