X3075

INTERSECTION OF X1X_3 AND X2X_255

X3075 = X3-gimel conjugate of X35
< 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) { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 29, 58 }: Central Line L(29, 58) { 2, 255 }: Central Line L(2, 255) { 47, 238 }: Central Line L(47, 238) { 4, 603 }: Central Line L(4, 603) { 109, 946 }: Central Line L(109, 946) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_2 = CENTROID (0.5374, 0.2000) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_4 = ORTHOCENTER (0.6122, 0.3958) X_603 = -CEVA CONJUGATE OF X(56) (0.5992, 0.1851) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_946 = MIDPOINT OF X(1) AND X(4) (0.5918, 0.3145) X_3075 = INTERSECTION OF X(1)X(3) AND X(2)X(255) (0.6061, 0.2970) A B C X1 X3 X29 X58 X2 X255 X47 X238 X4 X603 X109 X946 X3075 (a, b, c) = (5, 6, 7) | AB = 1

X3075 (INTERSECTION OF X1X_3 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): \(3.476896309596\)
▸ Incident Central Lines18 lines

{1, 3}, {2, 255}, {4, 603}, {5, 1935}, {11, 1399}, {29, 58}, {47, 238}, {81, 1816}, {109, 946}, {158, 1430}, {222, 1745}, {389, 1364}, {412, 1785}, {750, 1406}, {1393, 1870}, {1699, 1777}, {3068, 3076}, {3069, 3077}

▸ Functional Relations2 relations