X3741

X321com[n(INCENTRAL)*n(MEDIAL)]

X3741 = complement of X42
< A B C >: Reference Triangle △ABC < M_a M_b M_c >: Medial Triangle △M_a M_b M_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 42 }: Nagel Line { 1, 2 }: Nagel Line { 116, 126 }: Central Line L(116, 126) { 38, 321 }: Central Line L(38, 321) { 256, 314 }: Central Line L(256, 314) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) M_a = Midpoint M_a of BC (0.8061, 0.2999) M_b = Midpoint M_b of CA (0.3061, 0.2999) M_c = Midpoint M_c of AB (0.5000, 0.0000) X_2 = CENTROID (0.5374, 0.2000) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_1 = INCENTER (0.5714, 0.2333) X_116 = MIDPOINT OF X(4) AND X(103) (0.6990, 0.0375) X_126 = -OF-MEDIAL-TRIANGLE (0.3119, 0.3228) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_314 = ISOTOMIC CONJUGATE OF X(65) (0.4457, 0.1206) X_3741 = com[n(INCENTRAL)*n(MEDIAL)] (0.5121, 0.1752) A B C Ma Mb Mc X2 X42 X1 X116 X126 X38 X321 X256 X314 X3741 (a, b, c) = (5, 6, 7) | AB = 1

X3741 (X321com[n(INCENTRAL)*n(MEDIAL)]) 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 \(f(a,b,c) = a(b^{2} + c^{2}) + bc(b + c)\)
Search Value (6, 9, 13): \(3.302111116091\)
▸ Incident Central Lines20 lines

{1, 2}, {11, 1211}, {31, 1150}, {38, 321}, {75, 982}, {116, 126}, {141, 674}, {226, 1469}, {238, 333}, {256, 314}, {312, 984}, {516, 1764}, {518, 1215}, {594, 1575}, {964, 1468}, {993, 1011}, {2238, 2300}, {2260, 2345}, {2276, 2321}, {3136, 3454}

▸ Functional Relations4 relations