X3026

10th STEVANOVIC POINT

< 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) { 150, 388 }: Central Line L(150, 388) { 274, 1682 }: Central Line L(274, 1682) { 1111, 1357 }: Central Line L(1111, 1357) { 1365, 1565 }: Central Line L(1365, 1565) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_150 = REFLECTION OF X(20) IN X(103) (1.1837, -0.4499) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5168, 0.1843) X_1682 = INSIMILICENTER(INCIRCLE, APOLLONIUS CIRCLE) (0.5367, 0.1744) X_1111 = TRILINEAR SQUARE OF X(514) (0.7470, 0.0849) X_1357 = BRISSE TRANSFORM OF X(100) (0.8000, 0.1866) X_1365 = BRISSE TRANSFORM OF X(110) (0.7771, 0.1231) X_1565 = ORTHOJOIN OF X(657) (0.7114, 0.0321) X_3026 = 10th STEVANOVIC POINT (0.7407, 0.0728) A B C X150 X388 X274 X1682 X1111 X1357 X1365 X1565 X3026 (a, b, c) = (5, 6, 7) | AB = 1

X3026 (10th STEVANOVIC POINT) 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 \(f(a,b,c) = bc(b + c - a)(b - c)^{2}(a^{2} + ab + ac + 2bc)^{2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.570624478008\)

X3026 lies on the incircle.

▸ Incident Central Lines4 lines

{150, 388}, {274, 1682}, {1111, 1357}, {1365, 1565}