Asquare is just big enough to contains a unit circle. what is radius of the largest circle in one of the corners in the square but outside the unit circle?

In that case, the radius of largest circle would be the hypotenuse & square's half sides would be the base & perimeter.

So, H² = 0.5²+0.5²
H² = 0.25 + 0.25
H² = 0.50
H = √0.50
H = 0.707 of unit value.

Radius & your final answer would be 0.707 of unit value.

Hope this helps!

The answer is