X3655

X2-EXTRAVERSION OF {X1, X2, X3}

< 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, 30 }: Central Line L(1, 30) { 2, 355 }: Central Line L(2, 355) { 3, 519 }: Central Line L(3, 519) { 376, 517 }: Central Line L(376, 517) { 381, 515 }: Central Line L(381, 515) { 549, 952 }: Central Line L(549, 952) 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_30 = EULER INFINITY POINT (0.7469, 0.7481) X_2 = CENTROID (0.5374, 0.2000) X_355 = FUHRMANN CENTER (0.5408, 0.2645) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_549 = MIDPOINT OF X(2) AND X(3) (0.5187, 0.1510) X_952 = INTERSECTION OF X(1)X(5) AND X(3)X(8) (0.1267, 0.6191) X_3655 = -EXTRAVERSION OF {X(1), X(2), X(3)} (0.5340, 0.1354) A B C X1 X30 X2 X355 X3 X519 X376 X517 X381 X515 X549 X952 X3655 (a, b, c) = (5, 6, 7) | AB = 1

X3655 (X2-EXTRAVERSION OF {X1, X2, X3}) 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 \(f(a,b,c) = bc(5a^{4} - b^{4} - c^{4} - 4a^{2}b^{2} - 4a^{2}c^{2} + 2b^{2}c^{2} + 3k)\), where \(k = a(b^{3} + c^{3} - a^{2}b - a^{2}c - b^{2}c - bc^{2} + 2abc)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(5.843302611165\)
▸ Linear Combinations1 combination
▸ Incident Central Lines12 lines

{1, 30}, {2, 355}, {3, 519}, {8, 3524}, {40, 1483}, {145, 3579}, {376, 517}, {381, 515}, {549, 952}, {1387, 3586}, {1482, 3534}, {1837, 3582}