Question 22
A triangle $ABC$ satisfies $|AB|+|AC|=3|BC|$. Let $T$ be the point on segment $AC$ such that $|AC|=4|AT|$. Let $K,L$ lie in the interiors of segments $AB,AC$, respectively, such that $KL\parallel BC$ and $KL$ is tangent to the incircle of triangle $ABC$. Let $S=BT\cap KL$. Determine the ratio $|SL|/|KL|$.
