X975

INTERSECTION OF LINES X1X_2 AND X3X_37

< 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, 2 }: Nagel Line { 3, 37 }: Central Line L(3, 37) { 28, 33 }: Central Line L(28, 33) { 9, 58 }: Central Line L(9, 58) { 57, 201 }: Central Line L(57, 201) { 46, 750 }: Central Line L(46, 750) 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_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_9 = MITTENPUNKT (0.5110, 0.1615) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_201 = -CEVA CONJUGATE OF X(12) (0.4897, 0.1062) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_750 = INTERSECTION OF LINES X(1)X(88) AND X(2)X(31) (0.5675, 0.2354) X_975 = INTERSECTION OF LINES X(1)X(2) AND X(3)X(37) (0.5597, 0.2218) A B C X1 X2 X3 X37 X28 X33 X9 X58 X57 X201 X46 X750 X975 (a, b, c) = (5, 6, 7) | AB = 1

X975 (INTERSECTION OF LINES X1X_2 AND X3X_37) 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 \(f(a,b,c) = a^{3} + a^{2}(b + c) + a(b^{2} + c^{2} + 4bc) + (b + c)^{3}\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(1.980628673295\)
▸ Incident Central Lines10 lines

{1, 2}, {3, 37}, {9, 58}, {28, 33}, {35, 968}, {46, 750}, {57, 201}, {72, 940}, {226, 1038}, {312, 1010}