The Point $C$ of the triangle $ABC$ lies on the perpendicular to $AB$ trough Point $T$. $\alpha$ is the angle $\angle BAC$. Point $D$ lies on a line with the $\angle CBD=\alpha$. The Point $E$ lies on the perpendicular to $AC$ trough $D$. Proof that $E$ is on $AB$ and stays the same, while moving $C$ on the perpendicular.
I prooved that $D$, $A$ and $E$ are on a Circle by using Thales's theorem (like in this picture). But now I stuck.