X3488

INTERSECTION OF LINES X1X_4 AND X8X_405

X3488 = reflection of X1056 in X1
< 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) { 1056, 1 }: Incenter–Orthocenter Line { 1, 4 }: Incenter–Orthocenter Line { 8, 405 }: Central Line L(8, 405) { 57, 376 }: Central Line L(57, 376) { 9, 519 }: Central Line L(9, 519) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1056 = POINT ALCYONE (0.5756, 0.2499) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_8 = NAGEL POINT (0.4694, 0.1333) X_405 = EULER LINE INTERCEPT OF LINE X(1)X(6) (0.5325, 0.1870) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_9 = MITTENPUNKT (0.5110, 0.1615) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_3488 = INTERSECTION OF LINES X(1)X(4) AND X(8)X(405) (0.5672, 0.2166) A B C X1056 X1 X4 X8 X405 X57 X376 X9 X519 X3488 (a, b, c) = (5, 6, 7) | AB = 1

X3488 (INTERSECTION OF LINES X1X_4 AND X8X_405) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1 + \cos A + \cos B + \cos C - \cos B \cos C\)
Search Value (6, 9, 13): \(2.087447480906\)
▸ Incident Central Lines9 lines

{1, 4}, {3, 938}, {8, 405}, {9, 519}, {20, 942}, {35, 1788}, {57, 376}, {387, 1104}, {952, 954}

▸ Functional Relations1 relation