Let $ABC$ be a triangle with $\angle CAB=60^{\circ}$ and with incenter $I$. Let points $D,E$ be on sides $AC,AB$, respectively, such that $BD$ and $CE$ are angle bisectors of angles $\angle ABC$ and $\angle BCA$, respectively. Show that $ID=IE$.
Source: Kosovo MO 2019 Grade 11, Problem 3
Tags: geometry, incenter, angle bisector
Let $ABC$ be a triangle with $\angle CAB=60^{\circ}$ and with incenter $I$. Let points $D,E$ be on sides $AC,AB$, respectively, such that $BD$ and $CE$ are angle bisectors of angles $\angle ABC$ and $\angle BCA$, respectively. Show that $ID=IE$.