X3686

X37com(EXTOUCH TRIANGLE)

X3686 = excentral-to-ABC barycentric image of X37
< A B C >: Reference Triangle △ABC < M_a M_b M_c >: Medial Triangle △M_a M_b M_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 3879 }: Central Line L(2, 3879) { 6, 10 }: Central Line L(6, 10) { 8, 9 }: Central Line L(8, 9) { 69, 142 }: Central Line L(69, 142) { 261, 284 }: Central Line L(261, 284) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) M_a = Midpoint M_a of BC (0.8061, 0.2999) M_b = Midpoint M_b of CA (0.3061, 0.2999) M_c = Midpoint M_c of AB (0.5000, 0.0000) X_2 = CENTROID (0.5374, 0.2000) X_3879 = com[INVERSE(n(3rd EULER TRIANGLE))] (0.6533, 0.3196) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_8 = NAGEL POINT (0.4694, 0.1333) X_9 = MITTENPUNKT (0.5110, 0.1615) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_261 = ISOTOMIC CONJUGATE OF X(12) (0.5072, 0.1625) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_3686 = com(EXTOUCH TRIANGLE) (0.4795, 0.1402) A B C Ma Mb Mc X2 X3879 X6 X10 X8 X9 X69 X142 X261 X284 X3686 (a, b, c) = (5, 6, 7) | AB = 1

X3686 (X37com(EXTOUCH 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 \(f(a,b,c) = (-a + b + c)(2a + b + c)\)
Search Value (6, 9, 13): \(4.308363322632\)
▸ Incident Central Lines27 lines

{1, 966}, {2, 1449}, {6, 10}, {8, 9}, {37, 519}, {44, 594}, {45, 3625}, {69, 142}, {72, 2262}, {75, 527}, {141, 3008}, {145, 3247}, {198, 956}, {239, 1654}, {261, 284}, {306, 2280}, {515, 573}, {553, 3578}, {604, 1150}, {965, 1210}, {997, 3554}, {1100, 1125}, {1107, 2092}, {1743, 2345}, {2238, 2300}, {2287, 2323}, {2324, 2654}

▸ Functional Relations2 relations