X3749

X1707com[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) { 200, 238 }: Central Line L(200, 238) { 100, 614 }: Central Line L(100, 614) { 345, 519 }: Central Line L(345, 519) { 63, 902 }: Central Line L(63, 902) { 9, 983 }: Central Line L(9, 983) 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_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_614 = INTERSECTION OF LINES X(1)X(2) AND X(11)X(33) (0.6310, 0.2916) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_902 = CROSSPOINT OF X(6) AND X(106) (1.2500, 1.2247) X_9 = MITTENPUNKT (0.5110, 0.1615) X_983 = ISOGONAL CONJUGATE OF X(982) (0.5890, 0.2731) X_3749 = com[n(MEDIAL)*n(INCENTRAL)] (0.6077, 0.2999) A B C X1 X3 X200 X238 X100 X614 X345 X519 X63 X902 X9 X983 X3749 (a, b, c) = (5, 6, 7) | AB = 1

X3749 (X1707com[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 \(f(a,b,c) = a(3a^{2} + b^{2} + c^{2} - 2ab - 2ac)\)
Search Value (6, 9, 13): \(0.975634209844\)
▸ Incident Central Lines15 lines

{1, 3}, {9, 983}, {31, 1331}, {43, 3158}, {63, 902}, {100, 614}, {200, 238}, {214, 1811}, {345, 519}, {518, 1707}, {612, 1621}, {943, 989}, {1279, 1376}, {1449, 2276}, {3011, 3434}