The rectangle is inscribed in a circle, the sides of which are 3 dm and 4 dm. Find the radius of the circle.

It is known from the condition that the rectangle is inscribed in a circle. It is also known that the sides of a rectangle are equal to 3 dm and 4 dm. And we need to find the radius of the circle.

We’ll start by remembering that the diagonal of a rectangle is the diameter of the circumscribed circle.

To find the radius, we need to divide the diameter by 2. To find the diagonal, apply the Pythagorean theorem to the triangle formed by the two sides and the diagonal of the rectangle.

We are looking for the diagonal as an unknown hypotenuse:

c ^ 2 = a ^ 2 + b ^ 2;

c = √ (3 ^ 2 + 4 ^ 2) = √ (9 + 16) = √25 = 5 dm.

R = 5: 2 = 2.5 dm.