Question 66
Let $ABC$ be an acute triangle with circumcircle $\Gamma$. Let $A_1$, $B_1$ and $C_1$ be respectively the midpoints of the arcs $BAC$, $CBA$ and $ACB$ of $\Gamma$. Show that the inradius of triangle $A_1B_1C_1$ is not less than the inradius of triangle $ABC$.