X1040

INTERSECTION OF LINES X1X_3 AND X2X_33

X1040 = crosssum of X33 and X34
< 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) { 2, 33 }: Central Line L(2, 33) { 20, 34 }: Central Line L(20, 34) { 63, 212 }: Central Line L(63, 212) { 78, 345 }: Central Line L(78, 345) { 21, 1039 }: Central Line L(21, 1039) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1041 = ISOGONAL CONJUGATE OF X(1040) (0.6147, 0.4401) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_2 = CENTROID (0.5374, 0.2000) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_212 = -CEVA CONJUGATE OF X(41) (0.4719, 0.0786) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_1039 = ISOGONAL CONJUGATE OF X(1038) (0.6094, 0.3672) X_1040 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(33) (0.4854, 0.0753) A B C X1041 X1 X3 X2 X33 X20 X34 X63 X212 X78 X345 X21 X1039 X1040 (a, b, c) = (5, 6, 7) | AB = 1

X1040 (INTERSECTION OF LINES X1X_3 AND X2X_33) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\cos A - \cos A \cos B \cos C : :\)
Search Value (6, 9, 13): \(3.698495011381\)
▸ Alternate Coordinates1 form

  • Trilinears: \(1 - \sec B \sec C : :\)

▸ Incident Central Lines11 lines

{1, 3}, {2, 33}, {4, 1074}, {20, 34}, {21, 1039}, {63, 212}, {78, 345}, {226, 990}, {243, 1096}, {497, 614}, {1068, 1076}

▸ Functional Relations4 relations