X3330

INTERSECTION OF LINES X4X_6 AND X44X_513

X3330 = X1294-Ceva conjugate of X55
< 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 { 37, 73 }: Central Line L(37, 73) { 44, 513 }: Central Line L(44, 513) { 198, 408 }: Central Line L(198, 408) { 651, 857 }: Central Line L(651, 857) { 9, 1745 }: Central Line L(9, 1745) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1294 = COLLINGS TRANSFORM OF X(122) (0.4267, -0.4030) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_198 = -CEVA CONJUGATE OF X(6) (0.4741, -0.0381) X_408 = EULER LINE INTERCEPT OF LINE X(73)X(228) (0.4882, 0.0713) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_857 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X(75) (-0.3133, -2.0259) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1745 = MIMOSA TRANSFORM OF X(255) (0.4689, -0.1747) X_3330 = INTERSECTION OF LINES X(4)X(6) AND X(44)X(513) (0.8420, 2.8077) A B C X1294 X55 X4 X6 X37 X73 X44 X513 X198 X408 X651 X857 X9 X1745 X3330 (a, b, c) = (5, 6, 7) | AB = 1

X3330 (INTERSECTION OF LINES X4X_6 AND X44X_513) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = (\cos C)(\sin 2A - \sin 2B) - (\cos B)(\sin 2C - \sin 2A)\)
Search Value (6, 9, 13): \(-4.107444161007\)
▸ Alternate Coordinates1 form

  • Trilinears: \((\sin A + \sin B + \sin C) \sec A - (\sec A + \sec B + \sec C) \sin A : :\)

▸ Incident Central Lines8 lines

{4, 6}, {9, 1745}, {37, 73}, {44, 513}, {198, 408}, {216, 1765}, {651, 857}, {1100, 2654}

▸ Functional Relations3 relations