X3502

ISOGONAL CONJUGATE OF X3494

X3502 is the isogonal conjugate of X3494.
< 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, 2896 }: Central Line L(1, 2896) { 39, 3496 }: Central Line L(39, 3496) { 384, 3494 }: Central Line L(384, 3494) { 3492, 3500 }: Central Line L(3492, 3500) { 3493, 3503 }: Central Line L(3493, 3503) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3494 = INTERSECTION OF LINES X(1)X(87) AND X(3)X(2053) (0.4381, 0.1402) X_1 = INCENTER (0.5714, 0.2333) X_2896 = ANTICOMPLEMENTARY CONJUGATE OF X(76) (0.4820, 0.1279) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_3496 = INTERSECTION OF LINES X(1)X(32) AND X(4)X(9) (0.4919, 0.1173) X_384 = THE CONWAY POINT: EULER LINE INTERCEPT OF LINE X(32)X(76) (0.5532, 0.2412) X_3492 = INTERSECTION OF LINES X(4)X(83) AND X(32)X(695) (0.5108, 0.0518) X_3500 = INTERSECTION OF LINES X(1)X(295) AND X(3)X(238) (0.5973, 0.2216) X_3493 = INTERSECTION OF LINES X(4)X(194) AND X(32)X(694) (1.2219, -0.1216) X_3503 = ISOGONAL CONJUGATE OF X(3495) (0.6309, 0.3425) X_3502 = ISOGONAL CONJUGATE OF X(3494) (0.6508, 0.3268) A B C X3494 X1 X2896 X39 X3496 X384 X3492 X3500 X3493 X3503 X3502 (a, b, c) = (5, 6, 7) | AB = 1

X3502 (ISOGONAL CONJUGATE OF X3494) 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 \(f(a,b,c) = (ab + ac - bc)/(a^{2} + b^{2} + c^{2} - ab - ac + bc) (E\). Danneels)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.151335958072\)

X3502 lies on the cubic Z(X384).

▸ Incident Central Lines5 lines

{1, 2896}, {39, 3496}, {384, 3494}, {3492, 3500}, {3493, 3503}

▸ Functional Relations1 relation