X2035

INSIMILICENTER(MOSES CIRCLE, 1st LEMOINE CIRCLE)

X2035 is the insimilicenter(moses circle, 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) { 3, 6 }: Brocard Axis { 1015, 1672 }: Central Line L(1015, 1672) { 1500, 1673 }: Central Line L(1500, 1673) { 1573, 1681 }: Central Line L(1573, 1681) { 1574, 1680 }: Central Line L(1574, 1680) { 1571, 1701 }: Central Line L(1571, 1701) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1015 = EXSIMILICENTER OF MOSES CIRCLE AND INCIRCLE (0.7982, 0.1348) X_1672 = INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.5619, 0.2116) X_1500 = INSIMILICENTER OF MOSES CIRCLE AND INCIRCLE (0.5747, 0.2319) X_1673 = EXSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.6607, 0.4358) X_1573 = INSIMILICENTER OF SPIEKER AND MOSES CIRCLES (0.5399, 0.1993) X_1681 = EXSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5004, 0.1824) X_1574 = EXSIMILICENTER OF SPIEKER AND MOSES CIRCLES (0.4596, 0.1333) X_1680 = INSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5289, 0.1837) X_1571 = INSIMILICENTER OF EXCENTRAL AND MOSES CIRCLES (0.5507, 0.1833) X_1701 = EXSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE) (0.5980, 0.2692) X_2035 = INSIMILICENTER(MOSES CIRCLE, 1st LEMOINE CIRCLE) (0.5656, 0.2104) A B C X3 X6 X1015 X1672 X1500 X1673 X1573 X1681 X1574 X1680 X1571 X1701 X2035 (a, b, c) = (5, 6, 7) | AB = 1

X2035 (INSIMILICENTER(MOSES CIRCLE, 1st LEMOINE 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 \(f(A,B,C) = \sin A + \sin(A + \omega ) - \sin(A - 2\omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(2.197950686397\)
▸ Alternate Coordinates1 form

  • Trilinears: \(2 \sin \omega \cos(A - \omega ) + \sin(A + \omega )\)

▸ Incident Central Lines7 lines

{3, 6}, {1015, 1672}, {1500, 1673}, {1571, 1701}, {1572, 1700}, {1573, 1681}, {1574, 1680}