X3587

INTERSECTION OF LINES X1X_3 AND X9X_30

< 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) { 9, 30 }: Central Line L(9, 30) { 63, 376 }: Central Line L(63, 376) { 84, 550 }: Central Line L(84, 550) { 582, 1453 }: Central Line L(582, 1453) { 20, 3219 }: Central Line L(20, 3219) 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_9 = MITTENPUNKT (0.5110, 0.1615) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_550 = MIDPOINT OF X(3) AND X(20) (0.4439, -0.0448) X_582 = HARMONIC OF X(500) (0.8750, 0.7214) X_1453 = -BETH CONJUGATE OF X(452) (0.6101, 0.2792) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_3219 = INTERSECTION OF LINES X(2)X(7) AND X(8)X(90) (0.4976, 0.1420) X_3587 = INTERSECTION OF LINES X(1)X(3) AND X(9)X(30) (0.4606, 0.0297) A B C X1 X3 X9 X30 X63 X376 X84 X550 X582 X1453 X20 X3219 X3587 (a, b, c) = (5, 6, 7) | AB = 1

X3587 (INTERSECTION OF LINES X1X_3 AND X9X_30) 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 \(f(a,b,c) = a^{6} - a^{4}(3b + c)(b + 3c) + a^{2}(3b^{4} + 3c^{4} + 2b^{2}c^{2} + 8bc^{3} + 8b^{3}c) - (b - c)^{4}(b + c)^{2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(9.465642226316\)
▸ Incident Central Lines10 lines

{1, 3}, {4, 3305}, {9, 30}, {20, 3219}, {63, 376}, {84, 550}, {515, 3358}, {582, 1453}, {1445, 3488}, {3306, 3524}