X1692

RADICAL TRACE OF CIRCUMCIRCLE AND 2nd LEMOINE CIRCLE

X1692 = 1st-Lemoine-circle-inverse of X32
< 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 { 114, 230 }: Central Line L(114, 230) { 184, 1196 }: Central Line L(184, 1196) { 51, 1501 }: Central Line L(51, 1501) { 115, 1503 }: Central Line L(115, 1503) { 698, 1569 }: Central Line L(698, 1569) 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_114 = KIEPERT ANTIPODE (0.3616, 0.4140) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_1196 = 3rd SARAGOSSA POINT OF X(25) (0.6432, 0.2801) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_1501 = TRILINEAR 5th POWER POINT (0.6596, 0.3922) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_1503 = POINT ARKAB (0.4818, -0.3843) X_698 = EVEN (- 4, - 2) INFINITY POINT (1.0503, 0.4852) X_1569 = MOSES-CIRCLE ANTIPODE OF X(115) (0.4049, 0.3772) X_1692 = RADICAL TRACE OF CIRCUMCIRCLE AND 2nd LEMOINE CIRCLE (0.7995, 0.5968) A B C X3 X6 X114 X230 X184 X1196 X51 X1501 X115 X1503 X698 X1569 X1692 (a, b, c) = (5, 6, 7) | AB = 1

X1692 (RADICAL TRACE OF CIRCUMCIRCLE AND 2nd LEMOINE CIRCLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(2 \sin(A - 2\omega ) + \sin(A + 2\omega ) - \sin A : :\)
Barycentrics: \(a^{2}(2a^{4} + b^{4} + c^{4} - a^{2}b^{2} - a^{2}c^{2} - 2b^{2}c^{2}) : :\)
Search Value (6, 9, 13): \(0.048311084180\)
▸ Linear Combinations1 combination
▸ Incident Central Lines8 lines

{3, 6}, {51, 1501}, {114, 230}, {115, 1503}, {184, 1196}, {698, 1569}, {1015, 1428}, {1627, 1994}

▸ Functional Relations19 relations