X398

CROSSPOINT OF X4 AND X18

X398 is the crosspoint of X4 and X18.
< 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 { 5, 14 }: Central Line L(5, 14) { 15, 18 }: Central Line L(15, 18) { 30, 62 }: Central Line L(30, 62) { 3, 395 }: Central Line L(3, 395) { 51, 463 }: Central Line L(51, 463) 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_18 = 2nd NAPOLEON POINT (0.4434, 0.1317) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_62 = ISOGONAL CONJUGATE OF X(18) (0.6446, 0.3409) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_395 = MIDPOINT OF X(14) AND X(16) (1.3794, 1.1048) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_463 = EULER LINE INTERCEPT OF LINE X(51)X(398) (0.6238, 0.4259) X_398 = CROSSPOINT OF X(4) AND X(18) (0.5945, 0.2099) A B C X4 X18 X6 X5 X14 X15 X30 X62 X3 X395 X51 X463 X398 (a, b, c) = (5, 6, 7) | AB = 1

X398 (CROSSPOINT OF X4 AND X18) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\cos(B - C) - 2 \cos(A - \pi /3) : :\)
Search Value (6, 9, 13): \(2.568413278975\)
▸ Incident Central Lines13 lines

{3, 395}, {4, 6}, {5, 14}, {13, 546}, {15, 18}, {16, 550}, {30, 62}, {51, 463}, {141, 633}, {184, 462}, {203, 496}, {524, 634}, {533, 636}

▸ Functional Relations2 relations

Notes

X398 is the pole of the Euler line wrt every conic passing through X14, X15, X18 and X61. (Randy Hutson, January 17, 2020)

X398 is the {X4,X6}-harmonic conjugate of X397.