Chords AB and AC of one circle are congruent and the length of each of them is 16 cm.

Chords AB and AC of one circle are congruent and the length of each of them is 16 cm. Find the radius of the circle if the arc BC is 120 degrees.

Since, by condition, the chords AB and AC are congruent, the central angles formed or equal.

Angle AOB = AOC.

Angle AOB = AOC = (360 – BOC) / 2 = (360 – 120) / 2 = 120.

Then the internal angles BAC = ABC = ACB = 120/2 = 60.

In the ABC triangle, all angles are 60, which means the triangle is equilateral, AB = BC = AC = 16 cm.

The radius of a circle circumscribed around a regular triangle is:

R = a * √3 / 3, where a is the length of the side of a regular triangle.

R = 16 * √3 / 3 cm.

Answer: The radius of the circle is 16 * √3 / 3 cm.