X1672

INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE)

X1672 is the insimilicenter(incircle, 1st Lemoine circle).
< 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, 182 }: Central Line L(1, 182) { 55, 1343 }: Central Line L(55, 1343) { 56, 1342 }: Central Line L(56, 1342) { 2, 1681 }: Central Line L(2, 1681) { 11, 1676 }: Central Line L(11, 1676) { 8, 1680 }: Central Line L(8, 1680) 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_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1343 = EXSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.6155, 0.2927) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_1342 = INSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.5319, 0.1548) X_2 = CENTROID (0.5374, 0.2000) X_1681 = EXSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5004, 0.1824) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_1676 = INSIMILICENTER(1st LEMOINE CIRCLE, NINE-POINT CIRCLE) (0.5533, 0.2188) X_8 = NAGEL POINT (0.4694, 0.1333) X_1680 = INSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5289, 0.1837) X_1672 = INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.5619, 0.2116) A B C X1 X182 X55 X1343 X56 X1342 X2 X1681 X11 X1676 X8 X1680 X1672 (a, b, c) = (5, 6, 7) | AB = 1

X1672 (INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1 + \cos(A - \omega ) : :\)
Search Value (6, 9, 13): \(2.353996997115\)
▸ Linear Combinations2 combinations
▸ Incident Central Lines16 lines

{1, 182}, {2, 1681}, {8, 1680}, {11, 1676}, {12, 1677}, {55, 1343}, {56, 1342}, {57, 1700}, {181, 1683}, {371, 2008}, {372, 2007}, {1015, 2035}, {1124, 1688}, {1335, 1687}, {1682, 1684}, {1697, 1701}