Italian geometry problem

Question

I have a geometry question which I have a lot of difficulty doing the question is in Italian and I can kind of understand it but it is still troubling me. could someone explain it to me please ? Here is what Google translate says :

Given an ABC triangle, the bisectors of the outer angles B and C lie on the opposite side of A with respect to BC. Let D be their intersection and E, F the intersections of the parallel to BC through D, with the extensions of the AB and AC sides. Show that EF = EB + FC.

Here is the original text :

Dato un triangolo ABC, si conducano le bisettrici degli angoli esterni B e C che giacciono sulla parte opposta di A rispetto a BC. Detta D l loro intersezione ed E, F i punti di incontro della parallela per D a BC con i prolungamenti dei lati AB e AC, dimostrare che EF = EB + FC.

Thank you in advance.

Answer 1

The triangles $BED$ and $CFD$ are isosceles.

Answer 2

Let $ABC$ be a triangle and let $D$ be the intersection of the external bisectors from $B$ and $C$.
Let $E,F$ be the intersections of the parallel to $BC$ through $D$ with the sides $AB$ and $AC$.
With such assumptions, $EF=EB+FC$.

Proof: trivial by angle chasing. Both $EBD$ and $FCD$ are isosceles triangles.