Question 3
Let $ABC$ be a triangle with $AB \neq AC$. Let $E$ be such that $AE = BE$ and $(BE)$ is perpendicular to $(BC)$, and let $F$ be such that $AF = CF$ and $(CF)$ is perpendicular to $(BC)$. Let $D$ be the point of $(BC)$ such that $(AD)$ is tangent to the circumcircle of $ABC$ at $A$.
Prove that the points $D$, $E$, $F$ are collinear.
Prove that the points $D$, $E$, $F$ are collinear.