ISL 2021 G4

Let $A B C D$ be a quadrilateral inscribed in a circle $\Omega$. Let the tangent to $\Omega$ at $D$ intersect the rays $B A$ and $B C$ at points $E$ and $F$, respectively. A point $T$ is chosen inside the triangle $A B C$ so that $T E \| C D$ and $T F \| A D$. Let $K \neq D$ be a point on the segment $D F$ such that $T D=T K$. Prove that the lines $A C, D T$ and $B K$ intersect at one point.