VIII.3

Part of Ukrainian TYM Qualifying - geometry

Problems(1)

max of p/R ( 1- r/3R )

Source: VIII All-Ukrainian Tournament of Young Mathematicians, Qualifying p3

Find the largest value of the expression

\frac{p}{R}\left( 1- \frac{r}{3R}\right)

p,R, r

is, respectively, the perimeter, the radius of the circumscribed circle and the radius of the inscribed circle of a triangle.

geometric inequalitygeometryUkrainian TYM