A rectangle is inscribed in a circle with a radius of 4cm. One of the angles between its diagonals

A rectangle is inscribed in a circle with a radius of 4cm. One of the angles between its diagonals is 60 degrees Find the area of a rectangle

In the triangle COD, OD = OC = R, and since the angle COD = 60, the triangle COD is equilateral CD = OC = OD = R = 4 cm.

In a right-angled triangle ACD, AD ^ 2 = AC ^ 2 – CD ^ 2 = 64 – R ^ 2 = 64 – 16 = 48.

АD = 4 * √3 cm.

Then Savsd = CD * A = 4 * 4 * √3 = 16 * √3 cm2.

Answer: The area of the rectangle is 16 * √3 cm2.