X229

X7-CEVA CONJUGATE OF X81

X229 = X7-Ceva conjugate of X81
< 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, 267 }: Central Line L(1, 267) { 21, 36 }: Central Line L(21, 36) { 28, 60 }: Central Line L(28, 60) { 65, 110 }: Central Line L(65, 110) { 58, 244 }: Central Line L(58, 244) 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_267 = ISOGONAL CONJUGATE OF X(191) (0.6207, 0.3648) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_60 = ISOGONAL CONJUGATE OF X(12) (0.5790, 0.2258) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_229 = -CEVA CONJUGATE OF X(81) (0.5961, 0.2991) A B C X1 X267 X21 X36 X28 X60 X65 X110 X58 X244 X229 (a, b, c) = (5, 6, 7) | AB = 1

X229 (X7-CEVA CONJUGATE OF X81) 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 \(f(a,b,c) = (v + w - u)/(b + c)\), \(u = u(a,b,c) = a(b + c - a)/(b + c)\), \(v = u(b,c,a)\), \(w = u(c,a,b)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.596004115866\)
▸ Incident Central Lines6 lines

{1, 267}, {21, 36}, {28, 60}, {58, 244}, {65, 110}, {593, 1104}

▸ Functional Relations2 relations