X1685

INSIMILICENTER(2nd LEMOINE CIRCLE, APOLLONIUS CIRCLE)

X1685 is the insimilicenter(2nd 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, 486 }: Central Line L(10, 486) { 181, 1124 }: Central Line L(181, 1124) { 1335, 1682 }: Central Line L(1335, 1682) { 43, 1702 }: Central Line L(43, 1702) { 1695, 1703 }: Central Line L(1695, 1703) 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_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.5846, 0.2489) X_1335 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(1124) (0.4024, 0.0326) X_1682 = INSIMILICENTER(INCIRCLE, APOLLONIUS CIRCLE) (0.5367, 0.1744) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_1702 = INSIMILICENTER(BEVAN CIRCLE, 2nd LEMOINE CIRCLE) (0.5639, 0.2047) X_1695 = INSIMILICENTER(BEVAN CIRCLE, APOLLONIUS CIRCLE) (0.3697, -0.1216) X_1703 = EXSIMILICENTER(BEVAN CIRCLE, 2nd LEMOINE CIRCLE) (0.6625, 0.3753) X_1685 = INSIMILICENTER(2nd LEMOINE CIRCLE, APOLLONIUS CIRCLE) (0.5565, 0.1953) A B C X3 X6 X10 X486 X181 X1124 X1335 X1682 X43 X1702 X1695 X1703 X1685 (a, b, c) = (5, 6, 7) | AB = 1

X1685 (INSIMILICENTER(2nd 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 \(f(a,b,c) = (r - s)\sin A - (r + s)\cos A\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.710626700156\)
▸ Incident Central Lines6 lines

{3, 6}, {10, 486}, {43, 1702}, {181, 1124}, {1335, 1682}, {1695, 1703}