X3378

COT(A - π/4) POINT

X3378 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) { 19, 91 }: Central Line L(19, 91) { 46, 486 }: Central Line L(46, 486) { 1, 1806 }: Central Line L(1, 1806) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3377 = TAN(A - π/4) POINT (0.7028, 0.4733) X_19 = CLAWSON POINT (0.6246, 0.4244) X_91 = ISOGONAL CONJUGATE OF X(47) (-0.0865, -0.0205) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_1 = INCENTER (0.5714, 0.2333) X_1806 = INVERSE MIMOSA TRANSFORM OF X(372) (0.5819, 0.2373) X_3378 = COT(A - π/4) POINT (-0.0762, -0.0141) A B C X3377 X19 X91 X46 X486 X1 X1806 X3378 (a, b, c) = (5, 6, 7) | AB = 1

X3378 (COT(A - π/4) 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 \(f(A,B,C) = \cot(A - \pi /4)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(1.553319457115\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (1 + \tan A)/(1 - \tan A)\)

▸ Incident Central Lines3 lines

{1, 1806}, {19, 91}, {46, 486}

▸ Functional Relations2 relations