X1328

ARCTAN(-3) KIEPERT POINT

The construction of X1328 is like that of X1327, but using internally positioned squares. See the reference
< 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, 486 }: Central Line L(30, 486) { 381, 485 }: Central Line L(381, 485) { 6, 1327 }: Central Line L(6, 1327) { 372, 1132 }: Central Line L(372, 1132) { 547, 1151 }: Central Line L(547, 1151) 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_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_485 = VECTEN POINT (0.5773, 0.2578) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1327 = ARCTAN(3) KIEPERT POINT (0.5967, 0.3083) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_1132 = ARCTAN(-2) KIEPERT POINT (0.8864, -0.3774) X_547 = MIDPOINT OF X(2) AND X(5) (0.5468, 0.2244) X_1151 = ISOGONAL CONJUGATE OF X(1131) (0.5483, 0.1819) X_1328 = ARCTAN(-3) KIEPERT POINT (0.4997, 1.5024) A B C X30 X486 X381 X485 X6 X1327 X372 X1132 X547 X1151 X1328 (a, b, c) = (5, 6, 7) | AB = 1

X1328 (ARCTAN(-3) KIEPERT POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/(\sin A - 3 \cos A) : :\)
Barycentrics: \(1/(3 S_{A} - S) : :\)
Search Value (6, 9, 13): \(9.986274208728\)
▸ Incident Central Lines5 lines

{6, 1327}, {30, 486}, {372, 1132}, {381, 485}, {547, 1151}

▸ Functional Relations3 relations

Notes

at X1321.