X990

INTERSECTION OF LINES X1X_7 AND X3X_37

X990 = complement, wrt hexyl triangle, of X12717
< 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, 7 }: Soddy Line { 3, 37 }: Central Line L(3, 37) { 33, 57 }: Central Line L(33, 57) { 58, 84 }: Central Line L(58, 84) { 165, 612 }: Central Line L(165, 612) { 6, 971 }: Central Line L(6, 971) 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_7 = GERGONNE POINT (0.5903, 0.2769) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_612 = INTERSECTION OF LINES X(1)X(2) AND X(9)X(31) (0.5582, 0.2203) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_971 = INTERSECTION OF LINES X(3)X(9) AND X(4)X(7) (0.6441, 0.7770) X_990 = INTERSECTION OF LINES X(1)X(7) AND X(3)X(37) (0.6104, 0.3234) A B C X1 X7 X3 X37 X33 X57 X58 X84 X165 X612 X6 X971 X990 (a, b, c) = (5, 6, 7) | AB = 1

X990 (INTERSECTION OF LINES X1X_7 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 \(f(a,b,c) = a^{5} - a^{4}(b + c) - 2a^{3}bc - a(b - c)^{2}(b^{2} + c^{2}) + (b - c)^{2}(b + c)^{3}\)
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): \(-1.386821299805\)
▸ Incident Central Lines7 lines

{1, 7}, {3, 37}, {6, 971}, {33, 57}, {58, 84}, {165, 612}, {226, 1040}

▸ Functional Relations1 relation

  • X990 = complement, wrt hexyl triangle, of X12717