X3336

INTERSECTION OF LINES X1X_3 AND X7X_498

X3336 = SS(A → 3A) of X1507
< 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, 3 }: OI Line (Incenter–Circumcenter Line) { 5, 79 }: Central Line L(5, 79) { 2, 191 }: Central Line L(2, 191) { 7, 498 }: Central Line L(7, 498) { 244, 595 }: Central Line L(244, 595) { 404, 758 }: Central Line L(404, 758) 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_3 = CIRCUMCENTER (0.5000, 0.1021) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_2 = CENTROID (0.5374, 0.2000) X_191 = -CEVA CONJUGATE OF X(1) (0.4859, 0.1209) X_7 = GERGONNE POINT (0.5903, 0.2769) X_498 = YFF CONCURRENT CONGRUENT CIRCLES POINT (0.5518, 0.2140) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_595 = 2nd HATZIPOLAKIS-YIU POINT (0.6456, 0.3307) X_404 = {X(2),X(3)}-HARMONIC CONJUGATE OF X(21) (0.5538, 0.2429) X_758 = EVEN (1, 3) INFINITY POINT (0.1821, -0.2671) X_3336 = INTERSECTION OF LINES X(1)X(3) AND X(7)X(498) (0.6341, 0.3483) A B C X1 X3 X5 X79 X2 X191 X7 X498 X244 X595 X404 X758 X3336 (a, b, c) = (5, 6, 7) | AB = 1

X3336 (INTERSECTION OF LINES X1X_3 AND X7X_498) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((a - b + c)(a + b - c)(a + b + c) - abc : :\)
Search Value (6, 9, 13): \(-0.134391829979\)
▸ Alternate Coordinates1 form

  • Trilinears: \(1 + 2 (\cos B + \cos C - \cos A) : :\)

X3336 lies on the Napoleon cubic.

▸ Incident Central Lines28 lines

{1, 3}, {2, 191}, {4, 1768}, {5, 79}, {7, 498}, {17, 1652}, {18, 1653}, {54, 3468}, {58, 1325}, {62, 2306}, {63, 1698}, {109, 1393}, {244, 595}, {269, 1079}, {404, 758}, {412, 1784}, {579, 1781}, {583, 2160}, {920, 1445}, {1046, 1054}, {1158, 1699}, {1210, 1770}, {1254, 1772}, {1478, 1788}, {1707, 1775}, {1727, 1836}, {3459, 3460}, {3461, 3462}

▸ Functional Relations6 relations