X2258

X2-ISOCONJUGATE OF X940

X2258 = crosspoint of X941 and X959
< 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) { 9, 42 }: Central Line L(9, 42) { 55, 213 }: Central Line L(55, 213) { 31, 284 }: Central Line L(31, 284) { 1, 333 }: Central Line L(1, 333) { 57, 959 }: Central Line L(57, 959) { 200, 872 }: Central Line L(200, 872) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2484 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, BEVAN CIRCLE} (-35.7273, 22.7135) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_9 = MITTENPUNKT (0.5110, 0.1615) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_1 = INCENTER (0.5714, 0.2333) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_959 = ISOGONAL CONJUGATE OF X(958) (0.6111, 0.3031) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_872 = INTERSECTION OF LINES X(37)X(42) AND X(43)X(75) (0.6029, 0.2656) X_2258 = -ISOCONJUGATE OF X(940) (0.5966, 0.2593) A B C X2484 X101 X9 X42 X55 X213 X31 X284 X1 X333 X57 X959 X200 X872 X2258 (a, b, c) = (5, 6, 7) | AB = 1

X2258 (X2-ISOCONJUGATE OF X940) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X940
Barycentrics: \(a^{2}/f(a,b,c) : :\)
Search Value (6, 9, 13): \(1.093270479658\)
▸ Incident Central Lines12 lines

{1, 333}, {6, 1402}, {9, 42}, {31, 284}, {55, 213}, {57, 959}, {200, 872}, {386, 1245}, {741, 931}, {869, 2319}, {1973, 2299}, {2308, 2364}

▸ Functional Relations4 relations

Notes

Let A3B3C3 be the 3rd Conway triangle. Let La be the trilinear polar of A3, and define Lb and Lc cyclically. Let A' = Lb∩Lc, and define B' and C' cyclically. The lines AA', BB', CC' concur in X2258. (Randy Hutson, December 10, 2016)