X989

ISOGONAL CONJUGATE OF X988

X989 is the isogonal conjugate of X988.
< 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) { 84, 171 }: Central Line L(84, 171) { 40, 256 }: Central Line L(40, 256) { 21, 612 }: Central Line L(21, 612) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_988 = INTERSECTION OF LINES X(1)X(3) AND X(9)X(39) (0.5598, 0.2120) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_40 = BEVAN POINT (0.4286, -0.0292) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_612 = INTERSECTION OF LINES X(1)X(2) AND X(9)X(31) (0.5582, 0.2203) X_989 = ISOGONAL CONJUGATE OF X(988) (0.5820, 0.2552) A B C X988 X84 X171 X40 X256 X21 X612 X989 (a, b, c) = (5, 6, 7) | AB = 1

X989 (ISOGONAL CONJUGATE OF X988) 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 \(f(a,b,c) = 1/[a^{3} - a^{2}(b + c) - (3a + b + c)(b^{2} + c^{2})]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(1.316455669063\)
▸ Incident Central Lines3 lines

{21, 612}, {40, 256}, {84, 171}

▸ Functional Relations1 relation