X3462

X5-CEVA CONJUGATE OF X4

X3462 = isogonal conjugate of X3463
< 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, 54 }: Central Line L(4, 54) { 2, 1075 }: Central Line L(2, 1075) { 233, 1249 }: Central Line L(233, 1249) { 499, 1148 }: Central Line L(499, 1148) { 195, 2121 }: Central Line L(195, 2121) { 3336, 3461 }: Central Line L(3336, 3461) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_4 = ORTHOCENTER (0.6122, 0.3958) X_54 = KOSNITA POINT (0.5880, 0.2176) X_2 = CENTROID (0.5374, 0.2000) X_1075 = -CEVA CONJUGATE OF X(4) (0.6630, 1.7036) X_233 = -CEVA CONJUGATE OF X(140) (0.5475, 0.2218) X_1249 = ISOGONAL CONJUGATE OF X(1073) (-0.9482, -15.9845) X_499 = {X(1),X(2)}-HARMONIC CONJUGATE OF X(498) (0.4458, 0.1102) X_1148 = YIU-HATZIPOLAKIS POINT (0.4716, -1.3697) X_195 = -CEVA CONJUGATE OF X(3) (0.6761, 0.3331) X_2121 = ISOGONAL CONJUGATE OF X(2120) (0.6451, 0.1816) X_3336 = INTERSECTION OF LINES X(1)X(3) AND X(7)X(498) (0.6341, 0.3483) X_3461 = ISOGONAL CONJUGATE OF X(3460) (0.6102, 0.2013) X_3462 = -CEVA CONJUGATE OF X(4) (0.4603, -0.7229) A B C X5 X4 X54 X2 X1075 X233 X1249 X499 X1148 X195 X2121 X3336 X3461 X3462 (a, b, c) = (5, 6, 7) | AB = 1

X3462 (X5-CEVA CONJUGATE OF X4) 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 \(f(a,b,c) = x(- x/u + y/v + z/w)\), where \(u : v : w\) = X5,\(x : y : z\) = X4
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-6.038835923464\)

X3462 lies on the Napoleon cubic.

▸ Incident Central Lines8 lines

{1, 3469}, {2, 1075}, {4, 54}, {5, 3463}, {195, 2121}, {233, 1249}, {499, 1148}, {3336, 3461}

▸ Functional Relations2 relations