MathDB

Two right-angled triangles

Source: French TST 2005 - pb 2

May 26, 2005

geometrycircumcircleperimeterinradiusinequalitiestrigonometryPythagorean Theorem

Problem Statement

Two right angled triangles are given, such that the incircle of the first one is equal to the circumcircle of the second one. Let

S

(respectively

S'

) be the area of the first triangle (respectively of the second triangle). Prove that

\frac{S}{S'}\geq 3+2\sqrt{2}