X1683

INSIMILICENTER(1st LEMOINE CIRCLE, APOLLONIUS CIRCLE)

X1683 is the insimilicenter(1st Lemoine circle, Apollonius 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 { 10, 1677 }: Central Line L(10, 1677) { 181, 1672 }: Central Line L(181, 1672) { 1673, 1682 }: Central Line L(1673, 1682) { 43, 1700 }: Central Line L(43, 1700) { 1695, 1701 }: Central Line L(1695, 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_10 = SPIEKER CENTER (0.5204, 0.1833) X_1677 = EXSIMILICENTER(1st LEMOINE CIRCLE, NINE-POINT CIRCLE) (0.6019, 0.7290) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_1672 = INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.5619, 0.2116) X_1673 = EXSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.6607, 0.4358) X_1682 = INSIMILICENTER(INCIRCLE, APOLLONIUS CIRCLE) (0.5367, 0.1744) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_1700 = INSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE) (0.5232, 0.1374) X_1695 = INSIMILICENTER(BEVAN CIRCLE, APOLLONIUS CIRCLE) (0.3697, -0.1216) X_1701 = EXSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE) (0.5980, 0.2692) X_1683 = INSIMILICENTER(1st LEMOINE CIRCLE, APOLLONIUS CIRCLE) (0.5110, 0.1202) A B C X3 X6 X10 X1677 X181 X1672 X1673 X1682 X43 X1700 X1695 X1701 X1683 (a, b, c) = (5, 6, 7) | AB = 1

X1683 (INSIMILICENTER(1st LEMOINE CIRCLE, APOLLONIUS 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 \(f(a,b,c) = s \cos(A -\omega /2) - r \sin(A - \omega /2)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(6.162614712303\)
▸ Incident Central Lines6 lines

{3, 6}, {10, 1677}, {43, 1700}, {181, 1672}, {1673, 1682}, {1695, 1701}