SSC MTS 6 Aug 2019 Shift 1 Paper

Let the side of the square be a.
Inradius of square = side of square/2 = a/2
⇒ Circumradius of square = diagonal of square/2
⇒ Circumradius of square = (√2 × side of square)/2 = (√2a)/2
⇒ Inradius of square : Circumradius of square = (a/2) : (√2a/2) = 1 : √2
∴ The ratio of the inradius and circumradius of a square is 1 : √2.