X3073

INTERSECTION OF X3X_238 AND X4X_31

< 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, 31 }: Central Line L(4, 31) { 1, 90 }: Central Line L(1, 90) { 5, 171 }: Central Line L(5, 171) { 3, 238 }: Central Line L(3, 238) { 2, 601 }: Central Line L(2, 601) { 20, 602 }: Central Line L(20, 602) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_1 = INCENTER (0.5714, 0.2333) X_90 = -CROSS CONJUGATE OF X(1) (0.1022, 0.0201) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_2 = CENTROID (0.5374, 0.2000) X_601 = INTERSECTION OF LINES X(3)X(31) AND X(55)X(255) (0.5761, 0.2252) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_602 = INTERSECTION OF LINES X(3)X(31) AND X(56)X(255) (0.8182, 0.6170) X_3073 = INTERSECTION OF X(3)X(238) AND X(4)X(31) (0.6275, 0.2588) A B C X4 X31 X1 X90 X5 X171 X3 X238 X2 X601 X20 X602 X3073 (a, b, c) = (5, 6, 7) | AB = 1

X3073 (INTERSECTION OF X3X_238 AND X4X_31) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sin^{2} A - \cos B \cos C : \sin^{2} B - \cos C \cos A : \sin^{2} C - \cos A \cos B\)
Barycentrics: \(\sin^{3} A - \sin A \cos B \cos C : \sin^{3} B - \sin B \cos C \cos A : \sin^{3} C - \sin C \cos A \cos B\)
Search Value (6, 9, 13): \(2.331482706559\)
▸ Incident Central Lines29 lines

{1, 90}, {2, 601}, {3, 238}, {4, 31}, {5, 171}, {11, 1399}, {20, 602}, {21, 1064}, {40, 1724}, {47, 1479}, {55, 3074}, {57, 1777}, {58, 946}, {104, 1201}, {109, 1210}, {255, 497}, {388, 1497}, {515, 595}, {516, 580}, {578, 2175}, {605, 1587}, {606, 1588}, {631, 748}, {651, 1066}, {774, 1870}, {943, 2293}, {1058, 1496}, {1460, 1598}, {1467, 2956}