X3044

INTERSECTION X54X_114∩X99X_184

< 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) { 54, 114 }: Central Line L(54, 114) { 99, 184 }: Central Line L(99, 184) { 98, 1147 }: Central Line L(98, 1147) { 49, 2782 }: Central Line L(49, 2782) { 215, 3023 }: Central Line L(215, 3023) { 542, 3043 }: Central Line L(542, 3043) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_54 = KOSNITA POINT (0.5880, 0.2176) X_114 = KIEPERT ANTIPODE (0.3616, 0.4140) X_99 = STEINER POINT (0.1109, 0.4322) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_98 = TARRY POINT (0.8891, -0.2281) X_1147 = ISOGONAL CONJUGATE OF X(847) (0.8329, 0.3027) X_49 = CENTER OF SINE-TRIPLE-ANGLE CIRCLE (0.6275, 0.1789) X_2782 = ISOGONAL CONJUGATE OF X(2698) (0.9849, -0.1797) X_215 = -CEVA CONJUGATE OF X(50) (0.4113, 0.3887) X_3023 = 7th STEVANOVIC POINT (0.7493, 0.0823) X_542 = DIRECTION OF VECTOR AX + BX + CX, where X = X(98) (0.1649, 0.6534) X_3043 = INTERSECTION X(4)X(110)∩X(74)X(184) (0.4742, 0.4540) X_3044 = INTERSECTION X(54)X(114)∩X(99)X(184) (0.8676, -0.0249) A B C X54 X114 X99 X184 X98 X1147 X49 X2782 X215 X3023 X542 X3043 X3044 (a, b, c) = (5, 6, 7) | AB = 1

X3044 (INTERSECTION X54X_114∩X99X_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 \(f(a,b,c) = a(a^{4} + b^{4} - a^{2}b^{2} - a^{2}c^{2})(a^{4} + c^{4} - a^{2}b^{2} - a^{2}c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.555875474571\)

X3044 lies on the sine-triple-angle circle.

▸ Incident Central Lines10 lines

{49, 2782}, {54, 114}, {98, 1147}, {99, 184}, {215, 3023}, {542, 3043}, {543, 3048}, {690, 3047}, {2477, 3027}, {2786, 3046}