X3367

CSC(A - 5π/12) POINT

X3367 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, 15 }: Central Line L(5, 15) { 14, 372 }: Central Line L(14, 372) { 17, 371 }: Central Line L(17, 371) { 18, 615 }: Central Line L(18, 615) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_62 = ISOGONAL CONJUGATE OF X(18) (0.6446, 0.3409) X_3366 = SEC(A - 5π/12) POINT (0.5541, 0.2200) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_17 = 1st NAPOLEON POINT (0.5666, 0.2383) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_18 = 2nd NAPOLEON POINT (0.4434, 0.1317) X_615 = ISOGONAL CONJUGATE OF X(589) (0.4337, 0.0885) X_3367 = CSC(A - 5π/12) POINT (0.5942, 0.8035) A B C X62 X3366 X5 X15 X14 X372 X17 X371 X18 X615 X3367 (a, b, c) = (5, 6, 7) | AB = 1

X3367 (CSC(A - 5π/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 \(f(A,B,C) = \csc(A - 5\pi /12)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(16.637409899754\)

X3367 lies on the Kiepert hyperbola.

▸ Incident Central Lines4 lines

{5, 15}, {14, 372}, {17, 371}, {18, 615}

▸ Functional Relations2 relations