Question 148
Let $ABC$ be a right triangle with the right angle at $C$. On the segment $BC$ choose a point $D$ different from $B$ and $C$. Denote the circumcircle of the triangle $ABD$ by $\mathcal{K}$. Let $T$ be a point on the side $AB$ such that $DT$ is perpendicular to $AB$. Let $E$ be the second intersection of the line $DT$ with $\mathcal{K}$, denote the intersection of lines $CT$ and $EB$ by $F$ and let the line $DF$ meet $\mathcal{K}$ again at $G$. Prove that triangles $CEF$ and $BEG$ are similar.