The median of a right-angled triangle, drawn to the hypotenuse, is 14 cm. Find the diameter of the circumscribed circle.

Since the triangle ABC is rectangular, the angle ACB inscribed in the circle = 90, then the degree measure of the arc AB = 2 * 9 = 180, and is equal to half the degree measure of the circle.

Then the hypotenuse AB of triangle ABC is the diameter of the circumscribed circle.

Since OS is the median of the triangle, then AO = AB = AB / 2 = R, and point O is the center of the circle, and then OС = R = 14 cm.

The diameter of the circumscribed circle is: D = AB = 2 * OС = 2 * 14 = 28 cm.

Answer: The diameter of the circumscribed circle is 28 cm.