X3392

CSC(A - π/12) POINT

X3392 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) { 5, 16 }: Central Line L(5, 16) { 13, 372 }: Central Line L(13, 372) { 18, 371 }: Central Line L(18, 371) { 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_61 = ISOGONAL CONJUGATE OF X(17) (0.5764, 0.2283) X_3391 = SEC(A - π/12) POINT (0.5994, 0.3186) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_18 = 2nd NAPOLEON POINT (0.4434, 0.1317) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) 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_3392 = CSC(A - π/12) POINT (0.5097, 0.1742) A B C X61 X3391 X5 X16 X13 X372 X18 X371 X485 X17 X615 X202 X1335 X3392 (a, b, c) = (5, 6, 7) | AB = 1

X3392 (CSC(A - π/12) 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 \(f(A,B,C) = \csc(A - \pi /12)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(4.042937232203\)

X3392 lies on the Kiepert hyperbola.

▸ Incident Central Lines6 lines

{5, 16}, {13, 372}, {17, 615}, {18, 371}, {18, 485}, {202, 1335}

▸ Functional Relations2 relations