X1327

ARCTAN(3) KIEPERT POINT

Let \(BB_{A}\)CAC be the external square on side BC, and define \(CC_{B}\)ABA and \(AA_{C}\)BCB cyclically. The lines ABBA, BCCB, CAAC form a triangle perspective to triangle ABC, and the perspector is X1327.
< 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) { 30, 485 }: Central Line L(30, 485) { 381, 486 }: Central Line L(381, 486) { 371, 1131 }: Central Line L(371, 1131) { 547, 1152 }: Central Line L(547, 1152) { 6, 1328 }: Central Line L(6, 1328) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_485 = VECTEN POINT (0.5773, 0.2578) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_1131 = ARCTAN(2) KIEPERT POINT (0.5904, 0.2888) X_547 = MIDPOINT OF X(2) AND X(5) (0.5468, 0.2244) X_1152 = ISOGONAL CONJUGATE OF X(1132) (-0.9520, -2.2961) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1328 = ARCTAN(-3) KIEPERT POINT (0.4997, 1.5024) X_1327 = ARCTAN(3) KIEPERT POINT (0.5967, 0.3083) A B C X30 X485 X381 X486 X371 X1131 X547 X1152 X6 X1328 X1327 (a, b, c) = (5, 6, 7) | AB = 1

X1327 (ARCTAN(3) KIEPERT POINT) 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 \(f(A,B,C) = 1/(\sin A + 3 \cos A)\)
Barycentrics: \(1/(3 S_{A} + S) : :\)
Search Value (6, 9, 13): \(-0.836464449506\)
▸ Incident Central Lines5 lines

{6, 1328}, {30, 485}, {371, 1131}, {381, 486}, {547, 1152}

▸ Functional Relations1 relation