X3304

INTERSECTION OF LINES X1X_3 AND X495X_499

X3304 = crosssum of X1 and X1697
< 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, 3338 }: OI Line (Incenter–Circumcenter Line) { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 11, 153 }: Central Line L(11, 153) { 106, 386 }: Central Line L(106, 386) { 474, 519 }: Central Line L(474, 519) 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_3338 = INTERSECTION OF LINES X(1)X(3) AND X(7)X(90) (0.5971, 0.2805) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_153 = REFLECTION OF X(20) IN X(100) (-0.1020, 1.1248) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_386 = INVERSE-IN-BROCARD-CIRCLE OF X(58) (0.5912, 0.2526) X_474 = EULER LINE INTERCEPT OF LINE X(10)X(56) (0.5441, 0.2176) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_3304 = INTERSECTION OF LINES X(1)X(3) AND X(495)X(499) (0.5843, 0.2569) A B C X1 X3338 X3 X11 X153 X106 X386 X474 X519 X3304 (a, b, c) = (5, 6, 7) | AB = 1

X3304 (INTERSECTION OF LINES X1X_3 AND X495X_499) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(3 - \cos A : 3 - \cos B : 3 - \cos C\)
Barycentrics: \((\sin A)(3 - \cos A) :(\sin B)(3 - \cos B) : (\sin C)(3 - \cos C)\)
Search Value (6, 9, 13): \(1.271640111945\)
▸ Alternate Coordinates2 forms

  • Trilinears: \(a (s (-a + b + c) + (a - b + c) (a + b - c)) : :\)

  • Trilinears: \(a ((a^{2} - b^{2} - c^{2} + 6 b c) : :\)

▸ Incident Central Lines18 lines

{1, 3}, {7, 1476}, {11, 153}, {12, 1056}, {31, 1616}, {33, 1398}, {106, 386}, {144, 1001}, {145, 1376}, {198, 1100}, {474, 519}, {495, 499}, {496, 546}, {529, 2478}, {575, 611}, {576, 613}, {1149, 1191}, {1201, 1696}

▸ Functional Relations4 relations