X3973

X3161com(EXCENTRAL TRIANGLE)

X3973 = isogonal conjugate of X36603
< 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 { 173, 363 }: Central Line L(173, 363) { 200, 902 }: Central Line L(200, 902) { 165, 2348 }: Central Line L(165, 2348) { 484, 2270 }: Central Line L(484, 2270) { 610, 2265 }: Central Line L(610, 2265) 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_173 = CONGRUENT ISOSCELIZERS POINT (0.5924, 0.2741) X_363 = EQUAL PERIMETERS ISOSCELIZER POINT (0.5347, 0.2024) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_902 = CROSSPOINT OF X(6) AND X(106) (1.2500, 1.2247) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_2348 = -ISOCONJUGATE OF X(1477) (2.6057, 1.8476) X_484 = 1st EVANS PERSPECTOR (2.0952, 3.0327) X_2270 = -ISOCONJUGATE OF X(963) (0.7148, 0.6331) X_610 = -CEVA CONJUGATE OF X(1) (0.4310, -0.2713) X_2265 = -ISOCONJUGATE OF X(953) (-3.6429, 5.2489) X_3973 = com(EXCENTRAL TRIANGLE) (0.2981, -0.0913) A B C X1 X6 X173 X363 X200 X902 X165 X2348 X484 X2270 X610 X2265 X3973 (a, b, c) = (5, 6, 7) | AB = 1

X3973 (X3161com(EXCENTRAL TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(3b +3c - 5a)\)
Search Value (6, 9, 13): \(26.622359023948\)
▸ Incident Central Lines15 lines

{1, 6}, {144, 3008}, {165, 2348}, {173, 363}, {200, 902}, {346, 3632}, {391, 3679}, {484, 2270}, {519, 3161}, {572, 3217}, {610, 2265}, {2163, 2297}, {2345, 3707}, {2347, 3730}, {2999, 3219}

▸ Functional Relations3 relations