X3047

INTERSECTION X54X_113∩X2X_98

X3047 = reflection of X3043 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) { 3043, 49 }: Central Line L(3043, 49) { 2, 98 }: Central Line L(2, 98) { 54, 113 }: Central Line L(54, 113) { 156, 265 }: Central Line L(156, 265) { 206, 895 }: Central Line L(206, 895) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3043 = INTERSECTION X(4)X(110)∩X(74)X(184) (0.4742, 0.4540) X_49 = CENTER OF SINE-TRIPLE-ANGLE CIRCLE (0.6275, 0.1789) X_2 = CENTROID (0.5374, 0.2000) X_98 = TARRY POINT (0.8891, -0.2281) X_54 = KOSNITA POINT (0.5880, 0.2176) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_156 = -OF-TANGENTIAL-TRIANGLE (0.6520, -0.1707) X_265 = REFLECTION OF X(3) IN X(125) (0.8606, -0.0500) X_206 = -CEVA CONJUGATE OF X(32) (0.5105, -0.2297) X_895 = ISOGONAL CONJUGATE OF X(468) (0.9484, -0.0134) X_3047 = INTERSECTION X(54)X(113)∩X(2)X(98) (0.7807, -0.0962) A B C X3043 X49 X2 X98 X54 X113 X156 X265 X206 X895 X3047 (a, b, c) = (5, 6, 7) | AB = 1

X3047 (INTERSECTION X54X_113∩X2X_98) 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 \(f(a,b,c) = a^{3}(a^{4} + b^{4} - c^{4} - 2a^{2}b^{2} + b^{2}c^{2})(a^{4} - b^{4} + c^{4} - 2a^{2}c^{2} + b^{2}c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.962046101610\)

X3047 lies on the sine-triple-angle circle.

▸ Incident Central Lines13 lines

{2, 98}, {49, 3043}, {54, 113}, {74, 1147}, {156, 265}, {193, 1177}, {206, 895}, {215, 3024}, {690, 3044}, {1112, 1994}, {2477, 3028}, {2774, 3046}, {2854, 3048}

▸ Functional Relations1 relation