X3682

X1715com(EXTOUCH TRIANGLE)

X3682 = X19-isoconjugate of X27
< 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, 2 }: Nagel Line { 3, 48 }: Central Line L(3, 48) { 72, 73 }: Central Line L(72, 73) { 56, 209 }: Central Line L(56, 209) { 276, 313 }: Central Line L(276, 313) { 9, 581 }: Central Line L(9, 581) 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_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_209 = -CEVA CONJUGATE OF X(37) (0.7303, 0.4592) X_276 = ISOGONAL CONJUGATE OF X(217) (0.5554, 0.2771) X_313 = ISOTOMIC CONJUGATE OF X(58) (0.4368, 0.1249) X_9 = MITTENPUNKT (0.5110, 0.1615) X_581 = ORTHOHARMONIC OF X(284) (0.5657, 0.2106) X_3682 = com(EXTOUCH TRIANGLE) (0.3587, 0.0249) A B C X1 X2 X3 X48 X72 X73 X56 X209 X276 X313 X9 X581 X3682 (a, b, c) = (5, 6, 7) | AB = 1

X3682 (X1715com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((\cos A) (\cot A) (b + c) : :\)
Barycentrics: \(a^{2}(b + c)(- a^{2} + b^{2} + c^{2})^{2} : :\)
Search Value (6, 9, 13): \(4.283731705488\)
▸ Incident Central Lines34 lines

{1, 2}, {3, 48}, {9, 581}, {20, 2947}, {35, 1819}, {56, 209}, {58, 2327}, {72, 73}, {97, 2169}, {100, 1816}, {101, 1297}, {210, 2594}, {226, 3191}, {238, 1612}, {255, 394}, {276, 313}, {283, 1794}, {326, 1264}, {329, 1745}, {518, 1066}, {580, 2323}, {603, 3173}, {758, 1042}, {901, 2755}, {908, 1838}, {960, 1064}, {1073, 1260}, {1217, 1826}, {1332, 1792}, {1472, 1918}, {1490, 2324}, {1780, 1801}, {2654, 3419}, {2939, 3101}

▸ Functional Relations5 relations