Question 57
Let $ABC$ be a right-angled triangle with the right angle at $C$, such that $|AC| = 2$ and $|BC| = 1$. A square is situated inside the triangle so that two of its vertices are on the side $AC$, the third one is on the side $AB$, and the fourth is on the circle of radius $1$ centred at $B$. Determine the length of the side of the square.