X988

INTERSECTION OF LINES X1X_3 AND X9X_39

X988 = isogonal conjugate of X989
< 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) { 9, 39 }: Central Line L(9, 39) { 38, 78 }: Central Line L(38, 78) { 84, 256 }: Central Line L(84, 256) { 21, 614 }: Central Line L(21, 614) { 404, 612 }: Central Line L(404, 612) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_989 = ISOGONAL CONJUGATE OF X(988) (0.5820, 0.2552) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_9 = MITTENPUNKT (0.5110, 0.1615) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_614 = INTERSECTION OF LINES X(1)X(2) AND X(11)X(33) (0.6310, 0.2916) X_404 = {X(2),X(3)}-HARMONIC CONJUGATE OF X(21) (0.5538, 0.2429) X_612 = INTERSECTION OF LINES X(1)X(2) AND X(9)X(31) (0.5582, 0.2203) X_988 = INTERSECTION OF LINES X(1)X(3) AND X(9)X(39) (0.5598, 0.2120) A B C X989 X1 X3 X9 X39 X38 X78 X84 X256 X21 X614 X404 X612 X988 (a, b, c) = (5, 6, 7) | AB = 1

X988 (INTERSECTION OF LINES X1X_3 AND X9X_39) 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 \(f(a,b,c) = a^{3} - a^{2}(b + c) - (3a + b + c)(b^{2} + c^{2})\)
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): \(2.067148796949\)
▸ Incident Central Lines8 lines

{1, 3}, {9, 39}, {21, 614}, {38, 78}, {77, 1106}, {84, 256}, {404, 612}, {936, 984}

▸ Functional Relations2 relations