Question 25
Let $ABCD$ be a cyclic quadrilateral with circumcircle $k$. The rays $\overrightarrow{DA}$ and $\overrightarrow{CB}$ meet at point $N$ and the line $NT$ is tangent to $k$, $T \in k$. The diagonals $AC$ and $BD$ meet at the centroid $P$ of $\triangle NTD$. Find the ratio $NT : AP$.