X1693

INSIMILICENTER(BROCARD CIRCLE,APOLLONIUS CIRCLE)

X1693 is the insimilicenter(Brocard 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, 1349 }: Central Line L(10, 1349) { 181, 1674 }: Central Line L(181, 1674) { 1675, 1682 }: Central Line L(1675, 1682) { 43, 1704 }: Central Line L(43, 1704) { 1695, 1705 }: Central Line L(1695, 1705) 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_1349 = EXSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5463, 0.1455) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_1674 = INSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.5563, 0.1989) X_1675 = EXSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.5349, 0.1503) X_1682 = INSIMILICENTER(INCIRCLE, APOLLONIUS CIRCLE) (0.5367, 0.1744) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_1704 = INSIMILICENTER(BEVAN CIRCLE, BROCARD CIRCLE) (0.5395, 0.1662) X_1695 = INSIMILICENTER(BEVAN CIRCLE, APOLLONIUS CIRCLE) (0.3697, -0.1216) X_1705 = EXSIMILICENTER(BEVAN CIRCLE, BROCARD CIRCLE) (0.5627, 0.2070) X_1693 = INSIMILICENTER(BROCARD CIRCLE,APOLLONIUS CIRCLE) (0.5357, 0.1610) A B C X3 X6 X10 X1349 X181 X1674 X1675 X1682 X43 X1704 X1695 X1705 X1693 (a, b, c) = (5, 6, 7) | AB = 1

X1693 (INSIMILICENTER(BROCARD 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 \(f(a,b,c) = e[2rs \sin A + (r^{2} - s^{2})\cos A] - (r^{2} + s^{2})\cos(A - \omega )\)
Search Value (6, 9, 13): \(5.704607426613\)
▸ Incident Central Lines6 lines

{3, 6}, {10, 1349}, {43, 1704}, {181, 1674}, {1675, 1682}, {1695, 1705}