Largest sphere radius that touches a wire in a cube

[thereddevils]

Homework Statement

A 100 mm cube has a thin and rigid wire inserted 20 mm from each of two adjacent edges ,as shown.The cube contains a sphere that is not cut by the wire .What is the largest possible radius ,to the nearest mm, of the sphere that just touches the wire?

Homework Equations

The Attempt at a Solution

Some hints ?

 

[LCKurtz]

Homework Statement

A 100 mm cube has a thin and rigid wire inserted 20 mm from each of two adjacent edges ,as shown.The cube contains a sphere that is not cut by the wire .What is the largest possible radius ,to the nearest mm, of the sphere that just touches the wire?

Homework Equations

The Attempt at a Solution

Some hints ?

Here's a top view, drawn to scale. That's my hint:

 

[thereddevils]

Here's a top view, drawn to scale. That's my hint:

that's a great hint, thanks! I got r=47mm by phythagoras.