X1467

X938-BETH CONJUGATE OF X938

X1467 = {X57,X1420}-harmonic conjugate of X3
< 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) { 34, 269 }: Central Line L(34, 269) { 7, 452 }: Central Line L(7, 452) { 207, 278 }: Central Line L(207, 278) { 142, 388 }: Central Line L(142, 388) { 604, 610 }: Central Line L(604, 610) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_938 = ANTICOMPLEMENT OF X(936) (0.5846, 0.2462) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_7 = GERGONNE POINT (0.5903, 0.2769) X_452 = -HIRST INVERSE OF X(449) (0.5268, 0.1722) X_207 = -CEVA CONJUGATE OF X(34) (0.5818, 0.9198) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_610 = -CEVA CONJUGATE OF X(1) (0.4310, -0.2713) X_1467 = -BETH CONJUGATE OF X(938) (0.6380, 0.3556) A B C X938 X1 X3 X34 X269 X7 X452 X207 X278 X142 X388 X604 X610 X1467 (a, b, c) = (5, 6, 7) | AB = 1

X1467 (X938-BETH CONJUGATE OF X938) 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 \(f(a,b,c) = (1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X938
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.161401770612\)
▸ Incident Central Lines11 lines

{1, 3}, {7, 452}, {28, 1412}, {34, 269}, {142, 388}, {207, 278}, {222, 1453}, {604, 610}, {614, 1042}, {1066, 1103}, {1104, 1394}

▸ Functional Relations1 relation