Let $ABC$ be a triangle, and let $DEF$ be another triangle inscribed in the incircle of $ABC$. If $s$ and $s_1$ denote the semiperimeters of $ABC$ and $DEF$ respectively, prove that $2s_1 \le s$. When does equality hold?
Problem
Source: Indian Postal Coaching 2009 set 3 p4
Tags: geometry, circumcircle, Triangles, perimeter, Geometric Inequalities