Find the side of the square if the radius of the circumscribed circle is 16.

Let’s connect the center of this circle with the vertices of a square inscribed in this circle.

Each such segment is the radius of the given circle and, according to the condition of the problem, the length of each such segment is 16.

Since the square has 4 vertices, there will be 4 such segments in total, and these segments will divide the square into 4 triangles.

All these 4 triangles will be equal to each other on three sides.

Therefore, the angle of each such triangle whose vertex is the center of the circle will be equal to 360/4 = 90 ° and applying the Pythagorean theorem, we can find the length of the side of the square:

√ (16 ^ 2 + 16 ^ 2) = √ (2 * 16 ^ 2) = 16√2.

Answer: 16√2.