The sides of the rectangle are 8 and 6 find the radius of the circle circumscribed about this rectangle

The sides of the rectangle are 8 and 6 find the radius of the circle circumscribed about this rectangle find the area of the quadrilateral. Its diagonals are perpendicular.

Let’s calculate the area of the rectangle:

S = ab = 8 * 6 = 48.

A rectangle inscribed in a circle will have opposite angles of 90 degrees. This means that the arcs on which they will be based have a degree measure equal to 180 °. From this we can conclude that both diagonals will be diameters for the circle.

Find the diagonal c by the Pythagorean theorem:

c = √ (8 ^ 2 + 6 ^ 2) = √ (64 + 36) = √100 = 10 – the diagonal of the rectangle, which will be the diameter of the circle, since it divides it in half (180О).

We get the radius:

R = D / 2 = 10/2 = 5.

Answer: 5.