X3020

4th STEVANOVIC POINT

Centers X3020-X3026 are points on the incircle, as noted by Milorad Stevanovic (Hyacinthos, Dec. 7-8, 2004)
< 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) { 1086, 3023 }: Central Line L(1086, 3023) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7687, 0.1000) X_3023 = 7th STEVANOVIC POINT (0.7493, 0.0823) X_3020 = 4th STEVANOVIC POINT (0.7047, 0.0418) A B C X1086 X3023 X3020 (a, b, c) = (5, 6, 7) | AB = 1

X3020 (4th STEVANOVIC POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (b + c - a)[(b - c)(b^{2} + c^{2} - bc)]^{2}\)
Search Value (6, 9, 13): \(2.856936084165\)

X3020 lies on the incircle.

▸ Incident Central Lines1 line

{1086, 3023}