MathDB

bc=8Rr

Source: Sharygin contest. The final raund. 2008. Grade 10. Second day. Problem 6

August 31, 2008

geometrycircumcircleinradiustrigonometrygeometry unsolved

Problem Statement

(B.Frenkin) The product of two sides in a triangle is equal to

8Rr

, where

R

and

r

are the circumradius and the inradius of the triangle. Prove that the angle between these sides is less than

60^{\circ}