X2091

2nd STEVANOVIC PERSPECTOR

The bisector AX1 of angle A meets the A-excircle in two points; let A' be the point closer to I, and define B' and C' cyclically. Then triangle A'B'C' is perspective to the intouch triangle, and the perspector is X2091. (Milorad Stevanovic, Hyacinthos #8088, 10/02/03)
< 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) incircle: Incircle of △ABC { 57, 173 }: Central Line L(57, 173) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_173 = CONGRUENT ISOSCELIZERS POINT (0.5924, 0.2741) X_2091 = 2nd STEVANOVIC PERSPECTOR (0.6089, 0.3026) A B C X1 X57 X173 X2091 (a, b, c) = (5, 6, 7) | AB = 1

X2091 (2nd STEVANOVIC PERSPECTOR) 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 \(f(a,b,c) = [1/(b + c - a)](\sin B/2 + \sin C/2) \sec A/2\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.435725558873\)
▸ Incident Central Lines2 lines

{7, 4146}, {57, 173}

▸ Functional Relations1 relation