Quadrilateral $ABCD$ is circumscribed around circle $k$. Gind the smallest possible value of $$\frac{AB + BC + CD + DA}{AC + BD}$$, as well as all quadrilaterals with the above property where it is reached.
Problem
Source: IFYM - XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade,finals p3
Tags: geometry, tangential quadrilateral, geometric inequality, tangential