Solution:** Since the rectangle is inscribed in the circle, its diagonal is the diameter of the circle. Using the Pythagorean theorem:

["Solution: Since the rectangle is inscribed in the circle, its diagonal is the diameter of the circle. Using the Pythagorean theorem:", "When a rectangle is inscribed in a circle, the rectangle’s diagonals are equal in length and coincide with the diameter of the circle. This geometric property stems from the fact that opposite angles in a rectangle are right angles, and the diagonals bisect each other at 90°, forming two congruent right triangles across the rectangle.", "Let the rectangle have side lengths $ a $ and $ b $. The length of the diagonal $ d $, which is also the diameter of the circumscribing circle, can be determined using the Pythagorean theorem:", "[\nd = \sqrt{a^2 + b^2}\n]", "Since the diameter is $ d $, the radius $ r $ of the circle is:", "[\nr = \frac{\sqrt{a^2 + b^2}}{2}\n]", "This relationship is fundamental in solving problems involving inscribed rectangles, such as finding circumradius, maximizing area, or verifying geometric constraints. By applying the Pythagorean theorem to the triangle formed by half the diagonal and the rectangle’s sides, we derive the diameter directly—connecting algebra, geometry, and practical geometry applications seamlessly.", "In summary, whenever a rectangle is perfectly fitted inside a circle, its diagonal serves as the key bridge between the rectangle’s dimensions and the circle’s circle — encapsulated simply yet powerfully by:", "[\nd = \sqrt{a^2 + b^2}\n]", "This formula is essential for students, engineers, and geometric problem solvers working with circles and rectangles."]