X3298

INTERSECTION OF LINES X485X_495 AND X486X_496

< 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, 495 }: Central Line L(485, 495) { 486, 496 }: Central Line L(486, 496) { 372, 999 }: Central Line L(372, 999) { 606, 1496 }: Central Line L(606, 1496) { 1151, 2067 }: Central Line L(1151, 2067) 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_495 = JOHNSON MIDPOINT (0.5666, 0.2382) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_496 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(495) (0.5843, 0.2201) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_999 = MIDPOINT OF X(1) AND X(57) (0.5926, 0.2722) X_606 = INTERSECTION OF LINES X(371)X(601) AND X(372)X(602) (0.4469, 0.0416) X_1496 = POINT BETELGEUSE I (0.5410, 0.1932) X_1151 = ISOGONAL CONJUGATE OF X(1131) (0.5483, 0.1819) X_2067 = POINT CAROLI II (0.5451, 0.1342) X_3298 = INTERSECTION OF LINES X(485)X(495) AND X(486)X(496) (0.5501, 0.2079) A B C X1 X6 X485 X495 X486 X496 X372 X999 X606 X1496 X1151 X2067 X3298 (a, b, c) = (5, 6, 7) | AB = 1

X3298 (INTERSECTION OF LINES X485X_495 AND X486X_496) 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): \(2.056540529042\)
▸ Incident Central Lines6 lines

{1, 6}, {372, 999}, {485, 495}, {486, 496}, {606, 1496}, {1151, 2067}