X2362

X2-ISOCONJUGATE OF X2066

X2362 = crosspoint of X4 and X1123
< 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) { 6, 19 }: Central Line L(6, 19) { 2, 176 }: Central Line L(2, 176) { 1, 372 }: Central Line L(1, 372) { 46, 371 }: Central Line L(46, 371) { 4, 1336 }: Central Line L(4, 1336) { 72, 1377 }: Central Line L(72, 1377) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1123 = PAASCHE POINT (0.5572, 0.2178) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_19 = CLAWSON POINT (0.6246, 0.4244) X_2 = CENTROID (0.5374, 0.2000) X_176 = EQUAL DETOUR POINT (0.5803, 0.2537) X_1 = INCENTER (0.5714, 0.2333) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_1336 = ISOGONAL CONJUGATE OF X(1335) (0.6230, 0.5188) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_1377 = INSIMILICENTER(2nd LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5443, 0.2084) X_2362 = -ISOCONJUGATE OF X(2066) (0.6022, 0.2813) A B C X4 X1123 X6 X19 X2 X176 X1 X372 X46 X371 X1336 X72 X1377 X2362 (a, b, c) = (5, 6, 7) | AB = 1

X2362 (X2-ISOCONJUGATE OF X2066) 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 X2066
Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)
Search Value (6, 9, 13): \(0.718616148882\)
▸ Alternate Coordinates1 form

  • Trilinears: \(1/[1 + \cot(A/2)] : 1/[1 + \cot(B/2)] : 1/[1 + \cot(C/2)]\) (M. Iliev, 4/12/07)

▸ Incident Central Lines15 lines

{1, 372}, {2, 176}, {4, 1336}, {6, 19}, {40, 2066}, {46, 371}, {57, 2067}, {72, 1377}, {81, 1805}, {485, 1737}, {517, 1124}, {606, 1451}, {942, 1335}, {1151, 1155}, {1702, 2093}

▸ Functional Relations2 relations