X539

DIRECTION OF VECTOR AX + BX + CX, where X = X54

X539 = isogonal conjugate of X2383
< 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) { 2, 54 }: Central Line L(2, 54) { 155, 195 }: Central Line L(155, 195) { 30, 511 }: Central Line L(30, 511) { 5, 1493 }: Central Line L(5, 1493) { 265, 1568 }: Central Line L(265, 1568) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_54 = KOSNITA POINT (0.5880, 0.2176) X_155 = EIGENCENTER OF ORTHIC TRIANGLE (1.1658, 0.5033) X_195 = -CEVA CONJUGATE OF X(3) (0.6761, 0.3331) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_1493 = NAPOLEON CROSSSUM (0.6321, 0.2753) X_265 = REFLECTION OF X(3) IN X(125) (0.8606, -0.0500) X_1568 = ORTHOJOIN OF X(800) (0.1362, -0.3019) X_539 = DIRECTION OF VECTOR AX + BX + CX, where X = X(54) (1.0917, 0.3927) A B C X2 X54 X155 X195 X30 X511 X5 X1493 X265 X1568 X539 (a, b, c) = (5, 6, 7) | AB = 1

X539 (DIRECTION OF VECTOR AX + BX + CX, where X = X54) 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 \(f(a,b,c) = (2ax - by - cz)/a\), \(x = x(A,B,C) = 1/\cos(B-C)\), \(y = x(B,C,A)\), \(z = x(C,A,B)\)
Barycentrics: \((a^{2} - b^{2} - c^{2}) (2 a^{8} - 4 a^{6} (b^{2} + c^{2}) + 3 a^{4} (b^{4} + c^{4}) - 2 a^{2} (b^{2} - c^{2})^{2} (b^{2} + c^{2}) + (b^{2} - c^{2})^{4}) : :\)

X539 lies on the line at infinity.

▸ Incident Central Lines8 lines

{2, 54}, {3, 3519}, {5, 1493}, {30, 511}, {113, 2914}, {155, 195}, {265, 1568}, {2072, 3292}

▸ Functional Relations1 relation