Largest circle in a rectangle

Question

A shaded circle just fits inside a 2m x 3m rectangle. What is the radius in metres, of the largest circle that will also fit inside the rectangle but will not intersect the shaded circle?

Answer 1

The answer is $r=4-2\sqrt 3$, since this solves $$ (1+r)^2=(2-r)^2+(1-r)^2 $$ which makes sense if we place the first circle so that it is centered at $(0,0)$ and the other circle with its center at distance $r$ from each of the sides from the corner at $(2,1)$.

The set of corners of the rectangle is $(-1,-1),(-1,1),(2,1),(2,-1)$ in my setup.

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