Question 183
Let $ABCD$ be a quadrilateral inscribed in a circle $\Omega$. Let the tangent to $\Omega$ at $D$ intersect the rays $BA$ and $BC$ at points $E$ and $F$, respectively. A point $T$ is chosen inside the triangle $ABC$ so that $TE \parallel CD$ and $TF \parallel AD$. Let $K \neq D$ be a point on the segment $DF$ such that $TD = TK$. Prove that the lines $AC, DT$ and $BK$ intersect at one point.