X3503

ISOGONAL CONJUGATE OF X3495

X3503 is the isogonal conjugate of X3495.
< 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) { 109, 1923 }: Central Line L(109, 1923) { 76, 3501 }: Central Line L(76, 3501) { 83, 3496 }: Central Line L(83, 3496) { 384, 3495 }: Central Line L(384, 3495) { 3493, 3502 }: Central Line L(3493, 3502) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3495 = INTERSECTION OF LINES X(32)X(983) AND X(39)X(256) (0.4713, 0.1344) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_1923 = BICENTRIC SUM OF PU(13) (0.6447, 0.3295) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_3501 = INTERSECTION OF LINES X(1)X(39) AND X(4)X(9) (0.5467, 0.2440) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) 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_3493 = INTERSECTION OF LINES X(4)X(194) AND X(32)X(694) (1.2219, -0.1216) X_3502 = ISOGONAL CONJUGATE OF X(3494) (0.6508, 0.3268) X_3503 = ISOGONAL CONJUGATE OF X(3495) (0.6309, 0.3425) A B C X3495 X1 X3 X109 X1923 X76 X3501 X83 X3496 X384 X3493 X3502 X3503 (a, b, c) = (5, 6, 7) | AB = 1

X3503 (ISOGONAL CONJUGATE OF X3495) 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 \(f(a,b,c) = [b^{2}c^{2} + c^{2}a^{2} + a^{2}b^{2} - abc(b + c - a)]/(b + c - a) (E\). Danneels)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.216204479988\)

X3503 lies on the cubic Z(X384).

▸ Incident Central Lines6 lines

{1, 3}, {76, 3501}, {83, 3496}, {109, 1923}, {384, 3495}, {3493, 3502}

▸ Functional Relations1 relation