Circles - Geometry - General Aptitude (GA) Previous Year Questions

The ratio of the area of the inscribed circle to the area of the circumscribed circle of an equilateral triangle is ______

Consider a string P of length \( l \) that is laid out as a straight-line segment. Another string K is laid out as a semicircular arc with string P as its diameter, as represented in Figure (i). When both the strings are shortened by a length \( x \) they can be re-arranged such that the shortened string K forms a full circle with the shortened string P as its diameter, as represented in Figure (ii). The value of \( x/l \) is ________