The rectangle is inscribed in a circle with a radius of 5 cm. One of the sides is 8 cm. Find the other sides.

It is known from the condition that the rectangle is inscribed in a circle with a radius of 5 cm. It is also known that one of the sides is 8 cm. In order to find the other side, we will proceed as follows.

Recall that the diameter of the circle circumscribed about the rectangle is the diameter of the rectangle. We know the radius, then the diameter is:

D = 2 * R = 2 * 5 = 10 cm.

Consider a right-angled triangle formed by the sides of a rectangle (legs) and a diagonal (hypotenuse).

We are looking for an unknown leg according to the Pythagorean theorem:

a = √ (c ^ 2 – b ^ 2) = √ (10 ^ 2 – 8 ^ 2) = √ (100 – 64) = √36 = 6 cm.