Question 17
Let $I$ be the incenter and $AD$ be a diameter of the circumcircle of a triangle $ABC$. If 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 the lines $EF$ and $DI$ are perpendicular.
$$
BE = CF = \frac{AB + BC + CA}{2},
$$
show that the lines $EF$ and $DI$ are perpendicular.