Question 56
Let $ABCD$ be a quadrilateral inscribed in a circle $\Omega$. The tangent to $\Omega$ at $D$ meets the rays $BA$ and $BC$ at points $E$ and $F$, respectively. A point $T$ is chosen inside triangle $ABC$ so that $TE \parallel CD$ and $TF \parallel AD$. Let $K \neq D$ be a point on segment $DF$ such that $TD = TK$.
Prove that the lines $AC$, $DT$ and $BK$ are concurrent.
Prove that the lines $AC$, $DT$ and $BK$ are concurrent.