X3990

X1841com[INVERSE(n(ORTHIC TRIANGLE))]

X3990 = X92-isoconjugate of X28
< 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, 6 }: Incenter–Symmedian Line { 71, 73 }: Central Line L(71, 73) { 48, 184 }: Central Line L(48, 184) { 275, 321 }: Central Line L(275, 321) { 287, 336 }: Central Line L(287, 336) { 326, 394 }: Central Line L(326, 394) 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_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_275 = CEVAPOINT OF ORTHOCENTER AND SYMMEDIAN POINT (0.6057, 0.3473) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_287 = -HIRST INVERSE OF X(98) (0.7437, -0.0511) X_336 = ISOTOMIC CONJUGATE OF X(240) (0.7020, -0.0409) X_326 = ISOTOMIC CONJUGATE OF X(158) (0.3354, 0.0219) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_3990 = com[INVERSE(n(ORTHIC TRIANGLE))] (0.4021, 0.0322) A B C X1 X6 X71 X73 X48 X184 X275 X321 X287 X336 X326 X394 X3990 (a, b, c) = (5, 6, 7) | AB = 1

X3990 (X1841com[INVERSE(n(ORTHIC TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((b + c) \cos^{2} A\)
Barycentrics: \(a^{3}(b + c)(b^{2} + c^{2} - a^{2})^{2} : :\)
Search Value (6, 9, 13): \(3.303080060228\)
▸ Incident Central Lines14 lines

{1, 6}, {48, 184}, {71, 73}, {255, 577}, {275, 321}, {287, 336}, {326, 394}, {517, 1841}, {604, 2198}, {836, 3682}, {919, 2749}, {1331, 2327}, {2269, 2288}, {3197, 3198}

▸ Functional Relations1 relation