Question 33
On the side $BC$ of a right triangle $ABC$ with the right angle at $C$, a point $D$ different from $B$ and $C$ is chosen. Denote by $\mathcal{K}$ the circumcircle of triangle $ABD$. Let $T$ be the point on the side $AB$ such that $DT$ is perpendicular to $AB$. The line $DT$ meets the circle $\mathcal{K}$ again at the point $E$. Denote the intersection of the lines $CT$ and $EB$ by $F$. The line $DF$ meets the circle $\mathcal{K}$ again at the point $G$. Prove that the triangles $CEF$ and $BEG$ are similar.