X3093

INTERSECTION OF LINES X2X_1578 AND X4X_6

X3093 = {X4,X6}-harmonic conjugate of X3092
< 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) { 4, 6 }: Van Aubel Line { 25, 372 }: Central Line L(25, 372) { 235, 486 }: Central Line L(235, 486) { 427, 485 }: Central Line L(427, 485) { 394, 638 }: Central Line L(394, 638) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3092 = INTERSECTION OF LINES X(2)X(1579) AND X(4)X(6) (0.6095, 0.3668) X_4 = ORTHOCENTER (0.6122, 0.3958) 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_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_235 = -CEVA CONJUGATE OF X(185) (0.6375, 0.4618) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_427 = COMPLEMENT OF X(22) (0.5990, 0.3610) X_485 = VECTEN POINT (0.5773, 0.2578) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_638 = ANTICOMPLEMENT OF X(372) (0.1827, -0.3137) X_3093 = INTERSECTION OF LINES X(2)X(1578) AND X(4)X(6) (0.6173, 0.4483) A B C X3092 X4 X6 X25 X372 X235 X486 X427 X485 X394 X638 X3093 (a, b, c) = (5, 6, 7) | AB = 1

X3093 (INTERSECTION OF LINES X2X_1578 AND X4X_6) 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 \(f(A,B,C) = \sin A - \sec A\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-1.148171058168\)
▸ Incident Central Lines16 lines

{2, 1578}, {4, 6}, {20, 1579}, {24, 1152}, {25, 372}, {33, 1124}, {34, 1335}, {235, 486}, {371, 1593}, {378, 1151}, {394, 638}, {427, 485}, {1378, 1861}, {1905, 2362}, {3068, 3088}, {3069, 3089}

▸ Functional Relations1 relation