X3731

X391com(EXCENTRAL TRIANGLE)

< 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 { 35, 198 }: Central Line L(35, 198) { 10, 346 }: Central Line L(10, 346) { 391, 519 }: Central Line L(391, 519) { 200, 756 }: Central Line L(200, 756) { 165, 846 }: Central Line L(165, 846) 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_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_198 = -CEVA CONJUGATE OF X(6) (0.4741, -0.0381) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_346 = ISOTOMIC CONJUGATE OF X(279) (0.3948, 0.0827) X_391 = INTERSECTION OF LINES X(2,6) AND X(8,9) (0.4857, 0.1443) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_756 = CROSSPOINT OF X(10) AND X(37) (0.5409, 0.1988) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_846 = 4th SHARYGIN POINT (0.5437, 0.1969) X_3731 = com(EXCENTRAL TRIANGLE) (0.5478, 0.2052) A B C X1 X6 X35 X198 X10 X346 X391 X519 X200 X756 X165 X846 X3731 (a, b, c) = (5, 6, 7) | AB = 1

X3731 (X391com(EXCENTRAL TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a(a - 3b - 3c) : :\)
Search Value (6, 9, 13): \(2.350760178715\)
▸ Incident Central Lines24 lines

{1, 6}, {2, 2415}, {3, 1696}, {10, 346}, {35, 198}, {71, 2093}, {101, 2268}, {106, 2297}, {165, 846}, {200, 756}, {281, 1785}, {344, 3619}, {391, 519}, {573, 1334}, {610, 3465}, {612, 902}, {966, 2321}, {1400, 3339}, {1698, 1738}, {1707, 1961}, {1742, 3062}, {2182, 3612}, {2285, 3361}, {2999, 3305}