X3390

SIN(A - π/12) POINT

X3390 and related points occupy Bernard Gibert’s Table 38. See the note at X3364.
< 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) { 3, 6 }: Brocard Axis { 13, 486 }: Central Line L(13, 486) { 18, 485 }: Central Line L(18, 485) { 17, 615 }: Central Line L(17, 615) { 202, 1335 }: Central Line L(202, 1335) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3392 = CSC(A - π/12) POINT (0.5097, 0.1742) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_18 = 2nd NAPOLEON POINT (0.4434, 0.1317) X_485 = VECTEN POINT (0.5773, 0.2578) X_17 = 1st NAPOLEON POINT (0.5666, 0.2383) X_615 = ISOGONAL CONJUGATE OF X(589) (0.4337, 0.0885) X_202 = -CEVA CONJUGATE OF X(15) (0.5962, 0.2697) X_1335 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(1124) (0.4024, 0.0326) X_3390 = SIN(A - π/12) POINT (0.6167, 0.2948) A B C X3392 X3 X6 X13 X486 X18 X485 X17 X615 X202 X1335 X3390 (a, b, c) = (5, 6, 7) | AB = 1

X3390 (SIN(A - π/12) POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sin(A - \pi /12) : :\)
Search Value (6, 9, 13): \(0.429519195010\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\cos(A - \pi /3) + \sin(A - \pi /3) : :\)

▸ Incident Central Lines5 lines

{3, 6}, {13, 486}, {17, 615}, {18, 485}, {202, 1335}

▸ Functional Relations5 relations