X1395

X25-BETH CONJUGATE OF X25

X1395 = X34-Ceva conjugate of X604
< 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) { 25, 31 }: Central Line L(25, 31) { 28, 34 }: Central Line L(28, 34) { 4, 171 }: Central Line L(4, 171) { 24, 602 }: Central Line L(24, 602) { 238, 459 }: Central Line L(238, 459) { 212, 573 }: Central Line L(212, 573) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_4 = ORTHOCENTER (0.6122, 0.3958) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6627, 0.5278) X_602 = INTERSECTION OF LINES X(3)X(31) AND X(56)X(255) (0.8182, 0.6170) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_459 = -CEVA CONJUGATE OF X(4) (0.5934, 0.8103) X_212 = -CEVA CONJUGATE OF X(41) (0.4719, 0.0786) X_573 = ORTHOHARMONIC OF X(58) (0.4486, 0.0172) X_1395 = -BETH CONJUGATE OF X(25) (0.6371, 0.5131) A B C X25 X31 X28 X34 X4 X171 X24 X602 X238 X459 X212 X573 X1395 (a, b, c) = (5, 6, 7) | AB = 1

X1395 (X25-BETH CONJUGATE OF X25) 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 \(u : v : w\) = X25
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.024304673225\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = \sin A \tan A \sin^{2}(A/2)\)

▸ Incident Central Lines15 lines

{4, 171}, {24, 602}, {25, 31}, {28, 34}, {32, 1402}, {56, 1472}, {108, 727}, {212, 573}, {238, 459}, {278, 985}, {427, 750}, {468, 748}, {607, 1200}, {1106, 1398}, {1416, 1435}

▸ Functional Relations4 relations