Problem

Source: Indian Postal Coaching 2007 set 3 p4

Tags: geometry, circumradius, circumcircle, angle bisector



Let $BE$ and $CF$ be the bisectors of $\angle B$ and $\angle C$ of a triangle $ABC$ whose incentre is $I$. Suppose $EF$, extended, meets the circumcircle of $ABC$ in $M,N$. Show that the circumradius of $MIN$ is twice that of $ABC$.