X3192

X29-CEVA CONJUGATE OF X19

X3192 = X29-Ceva conjugate of X19
< 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) { 6, 25 }: Central Line L(6, 25) { 33, 42 }: Central Line L(33, 42) { 24, 58 }: Central Line L(24, 58) { 73, 208 }: Central Line L(73, 208) { 4, 386 }: Central Line L(4, 386) { 1, 406 }: Central Line L(1, 406) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_19 = CLAWSON POINT (0.6246, 0.4244) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6627, 0.5278) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_208 = -CEVA CONJUGATE OF X(34) (0.6242, -0.2728) X_4 = ORTHOCENTER (0.6122, 0.3958) X_386 = INVERSE-IN-BROCARD-CIRCLE OF X(58) (0.5912, 0.2526) X_1 = INCENTER (0.5714, 0.2333) X_406 = EULER LINE INTERCEPT OF LINE X(10)X(33) (0.5745, 0.2970) X_3192 = -CEVA CONJUGATE OF X(19) (0.5632, 0.0629) A B C X29 X19 X6 X25 X33 X42 X24 X58 X73 X208 X4 X386 X1 X406 X3192 (a, b, c) = (5, 6, 7) | AB = 1

X3192 (X29-CEVA CONJUGATE OF X19) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X29 and \(u : v : w\) = X19
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\), where \(f(a,b,c) = u(-u/x + v/y + w/z)\)
Search Value (6, 9, 13): \(0.856740349176\)
▸ Incident Central Lines21 lines

{1, 406}, {4, 386}, {6, 25}, {19, 2258}, {24, 58}, {31, 1182}, {33, 42}, {34, 1193}, {53, 430}, {55, 3195}, {73, 208}, {162, 2185}, {199, 577}, {216, 1011}, {235, 1834}, {387, 3089}, {461, 1249}, {475, 3216}, {581, 3194}, {995, 1870}, {2207, 2271}

▸ Functional Relations1 relation