Question 6
Let $I$ be the incenter of a triangle $ABC$. Let $D$ be the point diametrically opposite to $A$ on the circumcircle. Suppose that the point $E$ on the ray $[BA)$ and the point $F$ on the ray $[CA)$ satisfy the condition
$$
BE = CF = \frac{AB + BC + CA}{2}.
$$
Show that $(EF) \perp (DI)$.
$$
BE = CF = \frac{AB + BC + CA}{2}.
$$
Show that $(EF) \perp (DI)$.