X1680

INSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE)

X1680 is the insimilicenter(1st Lemoine circle, Spieker 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) { 10, 182 }: Central Line L(10, 182) { 2, 1673 }: Central Line L(2, 1673) { 8, 1672 }: Central Line L(8, 1672) { 958, 1343 }: Central Line L(958, 1343) { 1342, 1376 }: Central Line L(1342, 1376) { 1329, 1676 }: Central Line L(1329, 1676) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_2 = CENTROID (0.5374, 0.2000) X_1673 = EXSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.6607, 0.4358) X_8 = NAGEL POINT (0.4694, 0.1333) X_1672 = INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.5619, 0.2116) X_958 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(12) (0.5166, 0.1682) X_1343 = EXSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.6155, 0.2927) X_1342 = INSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.5319, 0.1548) X_1376 = EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER CIRCLE) (0.5265, 0.2074) X_1329 = COMPLEMENTARY CONJUGATE OF X(1) (0.4903, 0.1280) X_1676 = INSIMILICENTER(1st LEMOINE CIRCLE, NINE-POINT CIRCLE) (0.5533, 0.2188) X_1680 = INSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5289, 0.1837) A B C X10 X182 X2 X1673 X8 X1672 X958 X1343 X1342 X1376 X1329 X1676 X1680 (a, b, c) = (5, 6, 7) | AB = 1

X1680 (INSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc[b + c + a \cos(A - \omega )]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = b + c + a \cos(A - \omega )\)
Search Value (6, 9, 13): \(3.239204561094\)
▸ Incident Central Lines14 lines

{2, 1673}, {8, 1672}, {9, 1701}, {10, 182}, {371, 2014}, {372, 2013}, {958, 1343}, {1329, 1676}, {1342, 1376}, {1377, 1688}, {1378, 1687}, {1573, 2036}, {1574, 2035}, {1700, 1706}