X3297

INTERSECTION OF LINES X485X_496 AND X486X_495

< 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, 6 }: Incenter–Symmedian Line { 485, 496 }: Central Line L(485, 496) { 486, 495 }: Central Line L(486, 495) { 371, 999 }: Central Line L(371, 999) { 605, 1496 }: Central Line L(605, 1496) { 1151, 2066 }: Central Line L(1151, 2066) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_485 = VECTEN POINT (0.5773, 0.2578) X_496 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(495) (0.5843, 0.2201) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_495 = JOHNSON MIDPOINT (0.5666, 0.2382) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_999 = MIDPOINT OF X(1) AND X(57) (0.5926, 0.2722) X_605 = INTERSECTION OF LINES X(371)X(602) AND X(372)X(601) (0.6106, 0.2829) X_1496 = POINT BETELGEUSE I (0.5410, 0.1932) X_1151 = ISOGONAL CONJUGATE OF X(1131) (0.5483, 0.1819) X_2066 = POINT CAROLI I (0.5679, 0.2199) X_3297 = INTERSECTION OF LINES X(485)X(496) AND X(486)X(495) (0.5800, 0.2434) A B C X1 X6 X485 X496 X486 X495 X371 X999 X605 X1496 X1151 X2066 X3297 (a, b, c) = (5, 6, 7) | AB = 1

X3297 (INTERSECTION OF LINES X485X_496 AND X486X_495) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(2 + \sin A : 2 + \sin B : 2 + \sin C\)
Barycentrics: \((2 + \sin A)(\sin A) : (2 + \sin B)(\sin B) : (2 + \sin C)(\sin C)\)
Search Value (6, 9, 13): \(1.511682985518\)
▸ Incident Central Lines6 lines

{1, 6}, {371, 999}, {485, 496}, {486, 495}, {605, 1496}, {1151, 2066}