Question

a square 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?

Answer 1

r = (√2-1)/(√2+1)

I hope this helps.

Answer 2

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!