X1600

POINT CHORT II

X1600 = anticomplement of X1592
< A B C >: Reference Triangle △ABC < K_a K_b K_c >: Anticomplementary Triangle △K_a K_b K_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 1592 }: Euler Line { 2, 3 }: Euler Line { 6, 589 }: Central Line L(6, 589) { 394, 1152 }: Central Line L(394, 1152) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) K_a = Anticomplementary Vertex K_a (1.6122, 0.5999) K_b = Anticomplementary Vertex K_b (-0.3878, 0.5999) K_c = Anticomplementary Vertex K_c (0.3878, -0.5999) X_2 = CENTROID (0.5374, 0.2000) X_1592 = POINT CHARA IV (0.4755, 0.0381) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_589 = 2nd KENMOTU-VAN LAMOEN POINT (0.6340, 0.4099) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_1152 = ISOGONAL CONJUGATE OF X(1132) (-0.9520, -2.2961) X_1600 = POINT CHORT II (0.6612, 0.5237) A B C Ka Kb Kc X2 X1592 X3 X6 X589 X394 X1152 X1600 (a, b, c) = (5, 6, 7) | AB = 1

X1600 (POINT CHORT II) 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 \(f(A,B,C) = \csc A - 2 \cos A\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(0.959010639321\)
▸ Incident Central Lines3 lines

{2, 3}, {6, 589}, {394, 1152}

▸ Functional Relations2 relations

Notes

As a point on the Euler line, X1600 has Shinagawa coefficients \((E - 2S, 2S)\).