X3195

X33-CEVA CONJUGATE OF X25

< 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, 33 }: Central Line L(6, 33) { 25, 31 }: Central Line L(25, 31) { 108, 222 }: Central Line L(108, 222) { 208, 221 }: Central Line L(208, 221) { 154, 478 }: Central Line L(154, 478) { 213, 607 }: Central Line L(213, 607) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_208 = -CEVA CONJUGATE OF X(34) (0.6242, -0.2728) X_221 = -CEVA CONJUGATE OF X(56) (0.5474, -0.0688) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_478 = CENTER OF YIU CONIC (0.5030, -0.3520) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_607 = ISOGONAL CONJUGATE OF X(348) (0.6187, 0.3865) X_3195 = -CEVA CONJUGATE OF X(25) (0.5902, -0.1825) A B C X33 X25 X6 X31 X108 X222 X208 X221 X154 X478 X213 X607 X3195 (a, b, c) = (5, 6, 7) | AB = 1

X3195 (X33-CEVA CONJUGATE OF X25) 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 \(x : y : z\) = X33 and \(u : v : w\) = X25
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): \(0.422457688977\)
▸ Incident Central Lines14 lines

{6, 33}, {25, 31}, {41, 3172}, {55, 3192}, {108, 222}, {154, 478}, {208, 221}, {213, 607}, {329, 3194}, {611, 1957}, {614, 1876}, {1193, 1593}, {1201, 1398}, {2187, 3209}

▸ Functional Relations3 relations