X3748

X1621com[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) { 210, 1001 }: Central Line L(210, 1001) { 42, 1279 }: Central Line L(42, 1279) { 105, 1255 }: Central Line L(105, 1255) { 672, 1100 }: Central Line L(672, 1100) { 518, 1621 }: Central Line L(518, 1621) 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_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_1001 = MIDPOINT OF X(1) AND X(9) (0.5412, 0.1974) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_1279 = MIDPOINT OF X(1) AND X(238) (1.0952, 0.8554) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_1255 = ISOGONAL CONJUGATE OF X(1100) (0.5639, 0.2247) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.9245, 2.2184) X_1100 = COMPLEMENT OF X(319) (0.5787, 0.2419) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_1621 = TCC-PERSPECTOR OF X(81) (0.5431, 0.1961) X_3748 = com[n(MEDIAL)*n(INCENTRAL)] (0.5659, 0.2231) A B C X1 X3 X210 X1001 X42 X1279 X105 X1255 X672 X1100 X518 X1621 X3748 (a, b, c) = (5, 6, 7) | AB = 1

X3748 (X1621com[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 \(f(a,b,c) = a(2a^{2} + b^{2} + c^{2} - 3ab - 3ac - 2bc)\)
Search Value (6, 9, 13): \(1.903031408036\)
▸ Incident Central Lines17 lines

{1, 3}, {37, 2280}, {42, 1279}, {105, 1255}, {210, 1001}, {226, 3058}, {390, 1836}, {518, 1621}, {672, 1100}, {910, 1953}, {954, 1864}, {968, 3242}, {1108, 2266}, {1362, 2772}, {1365, 3021}, {1453, 2334}, {1962, 2611}