X1588

POINT CASTOR II

< 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) { 4, 6 }: Van Aubel Line { 2, 371 }: Central Line L(2, 371) { 20, 372 }: Central Line L(20, 372) { 194, 488 }: Central Line L(194, 488) { 193, 638 }: Central Line L(193, 638) { 615, 631 }: Central Line L(615, 631) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2 = CENTROID (0.5374, 0.2000) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_488 = ANTICOMPLEMENT OF X(485) (0.4576, 0.0844) X_193 = -CEVA CONJUGATE OF X(2) (0.7878, 0.4690) X_638 = ANTICOMPLEMENT OF X(372) (0.1827, -0.3137) X_615 = ISOGONAL CONJUGATE OF X(589) (0.4337, 0.0885) X_631 = 3/5*OG (0.5224, 0.1608) X_1588 = POINT CASTOR II (0.5955, 0.2203) A B C X4 X6 X2 X371 X20 X372 X194 X488 X193 X638 X615 X631 X1588 (a, b, c) = (5, 6, 7) | AB = 1

X1588 (POINT CASTOR 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 \(f(A,B,C) = \sin A - \cos B \cos C\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(2.315478875378\)
▸ Incident Central Lines13 lines

{2, 371}, {4, 6}, {20, 372}, {193, 638}, {194, 488}, {376, 1152}, {388, 1124}, {394, 1588}, {485, 1132}, {497, 1335}, {615, 631}, {640, 1271}, {1131, 1328}