Prove that angles in a circle equal each other

Question

Let a circle in the Euclidean plane be given, let $AB$ be a diameter, and let $CD$ be the tangent through point $A$. Let $E$ and $F$ be two points on the circle, on the same side of $AB$ as $C$, and with $F$ between $E$ and $A$.

Show that angle$AFE$= angle$DAE$

Answer 1

Let $\angle DAE=\alpha$, then $\angle EAC= 180-\alpha$, so the arc $AFE= 2(180-\alpha)$, so the arc $EBA=360-AFE=2\alpha$, then $2\alpha=EBA=2\angle AFE$ so $\angle AFE=\alpha=\angle DAE$

$\textbf{Note:}$ $\angle DAF =\alpha$ (green shadow) and $\angle FAC= 180-\alpha$ (black shadow)