Problem

Source: French TST 2005 - pb 2

Tags: geometry, circumcircle, perimeter, inradius, inequalities, trigonometry, Pythagorean Theorem



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