X1058

POINT ALKALUROPS

X1058 = isogonal conjugate of X1059
< 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) { 1, 4 }: Incenter–Orthocenter Line { 3, 390 }: Central Line L(3, 390) { 8, 392 }: Central Line L(8, 392) { 56, 376 }: Central Line L(56, 376) { 2, 496 }: Central Line L(2, 496) { 149, 377 }: Central Line L(149, 377) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1059 = ISOGONAL CONJUGATE OF X(1058) (0.5764, 0.2549) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_390 = REFLECTION OF GERGONNE POINT IN INCENTER (0.5526, 0.1897) X_8 = NAGEL POINT (0.4694, 0.1333) X_392 = X(1,6)∩X(10,11) (0.5265, 0.1800) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_2 = CENTROID (0.5374, 0.2000) X_496 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(495) (0.5843, 0.2201) X_149 = REFLECTION OF X(20) IN X(104) (1.3265, -0.3333) X_377 = EULER LINE INTERCEPT OF LINE X(7)X(8) (0.5473, 0.2258) X_1058 = POINT ALKALUROPS (0.5662, 0.2123) A B C X1059 X1 X4 X3 X390 X8 X392 X56 X376 X2 X496 X149 X377 X1058 (a, b, c) = (5, 6, 7) | AB = 1

X1058 (POINT ALKALUROPS) 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 \(f(A,B,C) = 2 - \cos B \cos C\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\sin A) f(A,B,C)\)
Search Value (6, 9, 13): \(2.135440105855\)
▸ Linear Combinations1 combination
▸ Incident Central Lines14 lines

{1, 4}, {2, 496}, {3, 390}, {8, 392}, {20, 999}, {29, 1057}, {55, 631}, {56, 376}, {149, 377}, {452, 956}, {517, 938}, {942, 962}, {943, 1001}, {1036, 1067}

▸ Functional Relations1 relation