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.
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
To fully earn your votes, here is an illustration:
To see the situation from arbitrary angles, consult the following dynamic 3D-graph:
GeoGebra-illustration
In particular, see what it looks like from above - the $1:4$ proportion of the overlap becomes evident!