Question 123
Given an acute triangle $ABC$ with $AB \lt BC \lt CA$. Let $D$ be a moving point on side $BC$, and $E$ be a moving point on the minor arc $\widehat{BC}$ of the circumcircle of $ABC$, such that $\angle BAD = \angle BED$.
Let $F$ be the intersection point of the line through $D$ perpendicular to $AB$ with the extension of $AC$. Prove that $\angle BEF$ is constant.
Let $F$ be the intersection point of the line through $D$ perpendicular to $AB$ with the extension of $AC$. Prove that $\angle BEF$ is constant.