NL-BXMO-TST 2021 Problem 5

Given is a triangle $ABC$ with the property that $|AB| + |AC| = 3|BC|$ . Let $T$ be the point on segment $AC$ such that $|AC| = 4|AT|$ . Let $K$ and $L$ be points on the interior of line segments $AB$ and $AC$ respectively such that $KL \parallel BC$ and $KL$ is tangent to the inscribed circle of $\vartriangle ABC$ . Let $S$ be the intersection of $BT$ and $KL$ . Determine the ratio $\frac{|SL|}{|KL|}$