Question 120
Let $A, B, C$ and $D$ be four points on a circle $\Omega$. Let $E$ and $F$ be the intersection points of the rays $[B A)$ and $[B C)$ with the tangent to $\Omega$ at $D$. Let $T$ be a point inside triangle $A B C$ such that $(T E)$ is parallel to $(C D)$ and $(T F)$ is parallel to $(A D)$. Finally, let $K$ be the point of the segment $[D F]$, other than $D$, such that $T D=T K$.
Prove that the lines $(A C),(D T)$ and $(B K)$ are concurrent.
Prove that the lines $(A C),(D T)$ and $(B K)$ are concurrent.