X618

COMPLEMENT OF X13

X618 is the complement of X13.
< 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) { 619, 620 }: Central Line L(619, 620) { 2, 13 }: Central Line L(2, 13) { 14, 99 }: Central Line L(14, 99) { 15, 298 }: Central Line L(15, 298) { 39, 395 }: Central Line L(39, 395) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_619 = COMPLEMENT OF X(14) (0.3494, 0.3571) X_620 = MIDPOINT OF X(618) AND X(619) (0.4308, 0.2580) X_2 = CENTROID (0.5374, 0.2000) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_99 = STEINER POINT (0.1109, 0.4322) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_298 = ISOTOMIC CONJUGATE OF 1st ISOGONIC CENTER (0.4724, 0.1301) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_395 = MIDPOINT OF X(14) AND X(16) (1.3794, 1.1048) X_618 = COMPLEMENT OF X(13) (0.5122, 0.1590) A B C X619 X620 X2 X13 X14 X99 X15 X298 X39 X395 X618 (a, b, c) = (5, 6, 7) | AB = 1

X618 (COMPLEMENT OF X13) 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 \(f(a,b,c) = [2S_{B}S_{C} + 5S_{A}a^{2} + 2 \sqrt{3}(b^{2} + c^{2}) \operatorname{area}]/a\)
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): \(3.906080612831\)
▸ Alternate Coordinates1 form

  • Trilinears: \(F(13)/a - \csc(A + \pi /3) : F(13)/b - \csc(B + \pi /3) : F(13)/c - \csc(C + \pi /3)\)

▸ Incident Central Lines11 lines

{2, 13}, {3, 635}, {5, 629}, {14, 99}, {15, 298}, {30, 623}, {39, 395}, {61, 627}, {140, 630}, {141, 542}, {396, 532}

▸ Functional Relations11 relations