X3043

INTERSECTION X4X_110∩X74X_184

X3043 = reflection of X3047 in X49
< 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) { 3047, 49 }: Central Line L(3047, 49) { 4, 110 }: Central Line L(4, 110) { 54, 125 }: Central Line L(54, 125) { 74, 184 }: Central Line L(74, 184) { 186, 323 }: Central Line L(186, 323) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3047 = INTERSECTION X(54)X(113)∩X(2)X(98) (0.7807, -0.0962) X_49 = CENTER OF SINE-TRIPLE-ANGLE CIRCLE (0.6275, 0.1789) X_4 = ORTHOCENTER (0.6122, 0.3958) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_54 = KOSNITA POINT (0.5880, 0.2176) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_186 = INVERSE-IN-CIRCUMCIRCLE OF X(4) (0.7957, 0.8758) X_323 = ISOTOMIC CONJUGATE OF X(94) (-0.8839, -1.3275) X_3043 = INTERSECTION X(4)X(110)∩X(74)X(184) (0.4742, 0.4540) A B C X3047 X49 X4 X110 X54 X125 X74 X184 X186 X323 X3043 (a, b, c) = (5, 6, 7) | AB = 1

X3043 (INTERSECTION X4X_110∩X74X_184) 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 \(f(a,b,c) = (1 - 4 \cos^{2} A)^{2} \sec A\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(4.565356306824\)

X3043 lies on the sine-triple-angle circle.

▸ Incident Central Lines14 lines

{4, 110}, {49, 3047}, {54, 125}, {74, 184}, {186, 323}, {215, 3028}, {378, 399}, {542, 3044}, {1614, 2777}, {1993, 2931}, {2477, 3024}, {2771, 3045}, {2772, 3046}, {2780, 3048}

▸ Functional Relations1 relation