# Thinking outside of the box

You want to draw a circle with a 4 inch radius. A trivial task for you and your trusty compass. When you go to grab your compass which has not had much love for a while you find it is rusted shut; stuck at 5 inches. Is it still possible to complete the task and draw a perfect circle with a 4-inch radius using the compass that can only draw circles with a 5-inch radius?

You may use other things as well to solve the problem such as a straightedge.

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you can if you have infinite time you can construct a segment of 4 inch distance, but not draw a circle of 4 inch so draw a circle of 5 inch and then in every direction draw a segment of four –  Willemien Feb 5 '14 at 23:49
No, you already answered the question for yourself. If it could draw a circle with a 4-inch radius, then it would not be a compass "that can only draw circles with a 5-inch radius", would it? –  Karl Kronenfeld Feb 6 '14 at 0:21

## My first approach

Yes, just place the center 3 inches above the paper. If that is a possibility?

## Different rendering

To put it differently, if you like, you could draw a 5-inch-circle, use scissors to cut a radius, then form a cone by overlapping at the cutting line until the proportion of the height to the radius of the base is 3 to 4...

That will happen when the overlap covers $\frac{1}{4}$ of the surface of the cone...

## Illustrations

In particular, see what it looks like from above - the $1:4$ proportion of the overlap becomes evident!