Question 13
In the triangle $ABC$ we have $|AB| \lt |AC|$. The bisectors of the angles at $B$ and $C$ meet $AC$ and $AB$ at $D$ and $E$ respectively. The lines $BD$ and $CE$ intersect at the incentre $I$ of $\triangle ABC$.
Prove that $\angle BAC = 60^\circ$ if and only if $|IE| = |ID|$.
Prove that $\angle BAC = 60^\circ$ if and only if $|IE| = |ID|$.