Geometric Inequalities

3abc a+b+c a+cos ẞ+cos a+sin ẞ+sin a²+b²+c² ABCD acute triangle Amer angles area DEF arithmetic-geometric mean arithmetic-geometric mean inequality b+c c+a a+b Beograd Bottema Canad Carlitz centre centroid circle circumcentre circumcircle convex cos² cosec Cosec cosec cotg cotg cotg2 denote Djordjević due to R. R. Elektrotehn Elem Equality holds Equality occurs equilateral triangle follows geometric incentre incircle inscribed intersection J. M. Child Kooistra Leuenberger Makowski Matematika v škole Math mean inequality midpoints min(b Monthly 68 Monthly 73 Moskva n-gon Nieuw Tijdschr Notae obtain obtuse triangles Oppenheim perimeter polygon quadrilateral R. R. Janić radius real numbers REMARK respectively second inequality sides BC sides of ABC Simon Stevin sin² Steinig tg a tg tg ẞ tg tg theorem triangle ABC triangle is equilateral vertices W. J. Blundon whence Wisk Zadači Živanović α β γ γ γ