What is the maximum possible radius of the inner circle in meters?

Question

An art museum wants to build a new gallery. They want the floor plan to be an annulus (a ring shape bounded by two concentric circles), with the outer circle having a radius of 10m.

If they can afford to hire only 4 guards, and every part of the gallery must be visible to at least one guard, then what is the maximum possible radius of the inner circle in meters?

Answer 1

The square constructed by joining four quadrant points of the outer circle has to be tangent to the inner circle making the radius of the inner circle to be 7.071 m