X2324

X2-ISOCONJUGATE OF X1413

X2324 = isogonal conjugate of X1422
< 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 { 77, 144 }: Central Line L(77, 144) { 33, 200 }: Central Line L(33, 200) { 40, 198 }: Central Line L(40, 198) { 78, 280 }: Central Line L(78, 280) { 41, 380 }: Central Line L(41, 380) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1422 = -BETH CONJUGATE OF X(189) (0.6044, 0.6471) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_144 = ANTICOMPLEMENT OF X(7) (0.4317, 0.0461) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_40 = BEVAN POINT (0.4286, -0.0292) X_198 = -CEVA CONJUGATE OF X(6) (0.4741, -0.0381) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_280 = -CROSS CONJUGATE OF X(8) (0.6379, 0.8041) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_380 = INTERSECTION OF LINES X(1)X(19) AND X(9)X(55) (0.5631, 0.2035) X_2324 = -ISOCONJUGATE OF X(1413) (0.3615, -0.0160) A B C X1422 X1 X6 X77 X144 X33 X200 X40 X198 X78 X280 X41 X380 X2324 (a, b, c) = (5, 6, 7) | AB = 1

X2324 (X2-ISOCONJUGATE OF X1413) 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 X1413
Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)
Search Value (6, 9, 13): \(4.942617245158\)
▸ Incident Central Lines18 lines

{1, 6}, {19, 1802}, {33, 200}, {40, 198}, {41, 380}, {65, 1696}, {77, 144}, {78, 280}, {101, 610}, {190, 326}, {223, 329}, {269, 527}, {394, 1422}, {517, 2270}, {579, 1467}, {936, 2345}, {1103, 2331}, {1195, 1334}

▸ Functional Relations4 relations

Notes

Let A'B'C' be the mixtilinear incentral triangle. Let La be the trilinear polar of A', and define Lb and Lc cyclically. Let A″ = Lb∩Lc, and define B″ and C″ cyclically. The lines AA″, BB″, CC″ concur in X2324. (Randy Hutson, January 15, 2019)