X1684

EXSIMILICENTER(1st LEMOINE CIRCLE, APOLLONIUS CIRCLE)

X1684 is the exsimilicenter(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, 1676 }: Central Line L(10, 1676) { 181, 1673 }: Central Line L(181, 1673) { 1672, 1682 }: Central Line L(1672, 1682) { 43, 1701 }: Central Line L(43, 1701) { 1695, 1700 }: Central Line L(1695, 1700) 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_1676 = INSIMILICENTER(1st LEMOINE CIRCLE, NINE-POINT CIRCLE) (0.5533, 0.2188) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_1673 = EXSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.6607, 0.4358) X_1672 = INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.5619, 0.2116) X_1682 = INSIMILICENTER(INCIRCLE, APOLLONIUS CIRCLE) (0.5367, 0.1744) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_1701 = EXSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE) (0.5980, 0.2692) X_1695 = INSIMILICENTER(BEVAN CIRCLE, APOLLONIUS CIRCLE) (0.3697, -0.1216) X_1700 = INSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE) (0.5232, 0.1374) X_1684 = EXSIMILICENTER(1st LEMOINE CIRCLE, APOLLONIUS CIRCLE) (0.6037, 0.2733) A B C X3 X6 X10 X1676 X181 X1673 X1672 X1682 X43 X1701 X1695 X1700 X1684 (a, b, c) = (5, 6, 7) | AB = 1

X1684 (EXSIMILICENTER(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 \(f(a,b,c) = r \cos(A -\omega /2) + s \sin(A - \omega /2)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.915870701084\)
▸ Incident Central Lines6 lines

{3, 6}, {10, 1676}, {43, 1701}, {181, 1673}, {1672, 1682}, {1695, 1700}