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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?

user341191
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    What have you tried so far? If you are struggling with it on a conceptual level, draw it out on a piece of grid paper. – DBPriGuy Nov 15 '16 at 19:51

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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.

enter image description here

String
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    This is good but i was wondering what was your thought process to go about this. Also how did you know this was going to be the biggest circle? I am trying to improve in problem solving and its so hard! – user341191 Nov 15 '16 at 20:36
  • @user341191: If you add some context to your question, such as your own thoughts and what you have tried, you can still avoid having it closed. I for one would retract my close vote :o) Then I can elaborate, if you like. – String Nov 15 '16 at 20:42
  • What programme did you use to draw this? – user341191 Nov 15 '16 at 21:07
  • @user341191: GeoGebra. Try plotting $f(x)=1-x^2/4$ and $g(x)=\sqrt{9-6x}$ together with the setup above. Those curves mean something in regards to the solution actually being optimal. – String Nov 15 '16 at 21:13