If the degree measure of the arc is 90 degrees, then find its chord along the given arc length.

Since, by condition, the degree measure of the arc AB is equal to 90, the central angle resting on this arc is also equal to 90.

Then triangle ABO is rectangular, and its chord AB is the hypotenuse of triangle AOB.

By the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = OA ^ 2 + OB ^ 2 = R ^ 2 + R ^ 2 = 2 * R ^ 2.

AB = R * √2 cm.

If the arc length AB = L is given, then L = π * R * 90/180 = π * R / 2.

Then R = 2 * L / π.

Then the chord AB = (2 * L / π) * √2 = 2 * √2 * L / π.

Answer: The chord length is 2 * √2 * L / π.