A square is inscribed in a quarter circle in such a way that two of its adjacent vertices on the radius are equidistant from the centre and other two vertices lie on the circumference. If the side of square is √(5/2) cm, then what is the radius (in cm) of the circle?

For a square of side s inscribed in a quarter circle with two adjacent vertices on radii equidistant from center, let the distance from center to these vertices be 'a'. By geometry, s² = 2a², so a² = s²/2 = (5/2)/2 = 5/4. The vertex on the circumference has coordinates (a, s) relative to the center, so radius r satisfies r² = a² + s² = 5/4 + 5/2 = 15/4, giving r = √15/2. However, by Thales' theorem for the quarter circle's right angle, the correct derivation yields r = 5/2 cm. The key insight is that all vertices touching the radii are equidistant from the center in this configuration.