X3074

INTERSECTION OF X1X_6 AND X2X_255

X3074 = {X2,X255}-harmonic conjugate of X3075
< 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) { 2, 255 }: Central Line L(2, 255) { 1, 6 }: Incenter–Symmedian Line { 4, 212 }: Central Line L(4, 212) { 47, 171 }: Central Line L(47, 171) { 10, 275 }: Central Line L(10, 275) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3075 = INTERSECTION OF X(1)X(3) AND X(2)X(255) (0.6061, 0.2970) X_2 = CENTROID (0.5374, 0.2000) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_4 = ORTHOCENTER (0.6122, 0.3958) X_212 = -CEVA CONJUGATE OF X(41) (0.4719, 0.0786) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_275 = CEVAPOINT OF ORTHOCENTER AND SYMMEDIAN POINT (0.6057, 0.3473) X_3074 = INTERSECTION OF X(1)X(6) AND X(2)X(255) (0.5060, 0.1556) A B C X3075 X2 X255 X1 X6 X4 X212 X47 X171 X10 X275 X3074 (a, b, c) = (5, 6, 7) | AB = 1

X3074 (INTERSECTION OF X1X_6 AND X2X_255) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\cos^{2} A + \sin B \sin C : \cos^{2} B + \sin C \sin A : \cos^{2} C + \sin A \sin B\)
Barycentrics: \((\sin A)(\cos^{2} A + \sin B \sin C) : (\sin B)(\cos^{2} B + \sin C \sin A) : (\sin C)(\cos^{2} C + \sin A \sin B)\)
Search Value (6, 9, 13): \(2.780223579616\)
▸ Incident Central Lines25 lines

{1, 6}, {2, 255}, {3, 1745}, {4, 212}, {5, 1936}, {10, 275}, {12, 2361}, {28, 2183}, {40, 1888}, {47, 171}, {55, 3073}, {73, 1006}, {165, 1777}, {191, 1735}, {201, 1870}, {226, 580}, {283, 908}, {388, 602}, {603, 631}, {1167, 1785}, {1698, 1771}, {1794, 1838}, {2182, 2939}, {3068, 3077}, {3069, 3076}

▸ Functional Relations1 relation