Santa gives his elves a task. He gives them a square paper, denoted as $ABCD$, with sidelength $\ell$. Santa has marked a point $E$ on segment $AB$ such that $AE = x$, where $x < \frac{\ell}{6}$ . Santa defines a “Christmas pentagon” as a pentagon where $4$ of the sides are tangent to a single circle and Santa calls the radius of this circle the “Christmas radius” of the pentagon. Santa asks his elves to construct the following figures by folding the paper, without other construction instruments: (1) a “Christmas pentagon” AND (2) a triangle with inradius $x$ and circumradius which is equal to the “Christmas radius” of the “Christmas pentagon” in (1). If the elves can do so, they can get an extra Chrismas gift from santa, which is a cute christmas frog. Help the elves to complete their task and prove that your method works.