X3008

(GERGONNE LINE)∩(NAGEL LINE)

X3008 = cevapoint of X1279 and X2348
< 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, 2 }: Nagel Line { 57, 169 }: Central Line L(57, 169) { 218, 226 }: Central Line L(218, 226) { 44, 527 }: Central Line L(44, 527) { 238, 516 }: Central Line L(238, 516) { 241, 514 }: Central Line L(241, 514) 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_2 = CENTROID (0.5374, 0.2000) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) X_218 = -CEVA CONJUGATE OF X(55) (0.6557, 0.3333) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_527 = DIRECTION OF VECTOR AX + BX + CX, where X = X(7) (0.8698, 0.6836) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_3008 = (GERGONNE LINE)∩(NAGEL LINE) (1.4558, 1.0998) A B C X1 X2 X57 X169 X218 X226 X44 X527 X238 X516 X241 X514 X3008 (a, b, c) = (5, 6, 7) | AB = 1

X3008 ((GERGONNE LINE)∩(NAGEL LINE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc[(b - c)^{2} + 2a^{2} - ab - ac]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-2.345112706814\)
▸ Incident Central Lines12 lines

{1, 2}, {44, 527}, {57, 169}, {101, 1429}, {190, 1266}, {218, 226}, {238, 516}, {241, 514}, {379, 1724}, {443, 1453}, {536, 2325}, {1445, 1723}

▸ Functional Relations9 relations