X3362

ISOGONAL CONJUGATE OF X1745

X3362 is the isogonal conjugate of X1745.
< 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) { 46, 296 }: Central Line L(46, 296) { 1, 1075 }: Central Line L(1, 1075) { 3, 1745 }: Central Line L(3, 1745) { 283, 1816 }: Central Line L(283, 1816) { 580, 1795 }: Central Line L(580, 1795) { 158, 2638 }: Central Line L(158, 2638) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) X_2638 = DIFFERENCE OF PU(77) (0.6093, 0.0064) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_296 = ISOGONAL CONJUGATE OF X(243) (0.7214, -0.0918) X_1 = INCENTER (0.5714, 0.2333) X_1075 = -CEVA CONJUGATE OF X(4) (0.6630, 1.7036) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1745 = MIMOSA TRANSFORM OF X(255) (0.4689, -0.1747) X_283 = -CROSS CONJUGATE OF X(21) (0.4475, 0.0704) X_1816 = INVERSE MIMOSA TRANSFORM OF X(1075) (0.4215, -0.1035) X_580 = ORTHOGONAL OF X(284) (0.7089, 0.4470) X_1795 = INVERSE MIMOSA TRANSFORM OF X(36) (0.7464, -0.0703) X_158 = -CROSS CONJUGATE OF X(92) (0.6215, 0.5117) X_3362 = ISOGONAL CONJUGATE OF X(1745) (0.6421, 1.3674) A B C X650 X2638 X46 X296 X1 X1075 X3 X1745 X283 X1816 X580 X1795 X158 X3362 (a, b, c) = (5, 6, 7) | AB = 1

X3362 (ISOGONAL CONJUGATE OF X1745) 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 \(f(A,B,C) = 1/(\sec B + \sec C - \sec A)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(5.868808418660\)

X3362 lies on the McKay cubic.

▸ Incident Central Lines8 lines

{1, 1075}, {3, 1745}, {46, 296}, {158, 2638}, {283, 1816}, {580, 1795}, {1069, 1936}, {1794, 2947}

▸ Functional Relations4 relations