Question 159
Let $T$ be the centroid of a triangle $ABC$. Consider two isosceles right-angled triangles $BTK$ and $CTL$ so that $K$ lies in the half-plane $BTC$ and $L$ lies in the half-plane $CTA$. Finally, denote the centre of the side $BC$ as $D$ and the centre of $KL$ as $E$. Determine all the possible values of the ratio $\frac{AT}{DE}$.