A square is inscribed in a circle with radius 20 cm. What is the measure of the side of the square?

To find the side of the square inscribed in a circle, we need to understand that the diameter of the circle is the diagonal of the square.

Step 1: We know that the radius of the circle is 20 cm, so the diameter of the circle (which is also the diagonal of the square) is 2 * radius = 2 * 20 cm = 40 cm.

Step 2: The diagonal of a square divides it into two congruent right triangles. So, we can use the Pythagorean theorem to find the side of the square. The theorem states that in a right triangle, the square of the length of the hypotenuse (diagonal in our case) is equal to the sum of the squares of the other two sides (which are equal in a square). So, if we let 'a' be the side of the square, we have:

a^2 + a^2 = diagonal^2 2a^2 = 40^2 a^2 = 40^2 / 2 a = sqrt(40^2 / 2)

Step 3: Calculate the value:

a = sqrt(1600) = 40 cm.

So, the side of the square is 40 cm.