X3477

ISOGONAL CONJUGATE OF X3475

X3477 is the isogonal conjugate of X3475.
< 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) { 77, 354 }: Central Line L(77, 354) { 78, 1001 }: Central Line L(78, 1001) { 3, 1471 }: Central Line L(3, 1471) { 1, 1827 }: Central Line L(1, 1827) { 219, 2280 }: Central Line L(219, 2280) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3475 = INTERSECTION OF LINES X(1)X(4) AND X(7)X(55) (0.5740, 0.2434) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_354 = WEILL POINT (0.5823, 0.2533) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_1001 = MIDPOINT OF X(1) AND X(9) (0.5412, 0.1974) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1471 = -BETH CONJUGATE OF X(1001) (0.6167, 0.3077) X_1 = INCENTER (0.5714, 0.2333) X_1827 = ZOSMA TRANSFORM OF X(7) (0.6082, 0.3740) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_2280 = -ISOCONJUGATE OF X(1002) (0.5750, 0.2304) X_3477 = ISOGONAL CONJUGATE OF X(3475) (0.5688, 0.2234) A B C X3475 X77 X354 X78 X1001 X3 X1471 X1 X1827 X219 X2280 X3477 (a, b, c) = (5, 6, 7) | AB = 1

X3477 (ISOGONAL CONJUGATE OF X3475) 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 \(f(A,B,C) = 1/(2 + \cos A + \cos B + \cos C + \cos B \cos C)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.928751898945\)
▸ Incident Central Lines5 lines

{1, 1827}, {3, 1471}, {77, 354}, {78, 1001}, {219, 2280}

▸ Functional Relations1 relation