Question 74
Let $I$ be the incenter and $AD$ a diameter of the circumcircle of triangle $ABC$. Let $E,F$ lie on the rays $BA,CA$, respectively, with
$$BE=CF=\frac{AB+BC+CA}{2}.$$
Prove that lines $EF$ and $DI$ intersect at right angles.
$$BE=CF=\frac{AB+BC+CA}{2}.$$
Prove that lines $EF$ and $DI$ intersect at right angles.