MathNet 2022-part-01 — 197 problems (EN–VI) Question 130

In a circle $k$ is inscribed $ABCD$, for which $S_{ACB} = s$, $S_{ACD} = t$, and $s \lt t$. Find the minimum of $A = \frac{4s^2 + t^2}{5st}$, and determine when it is achieved.