The radius of the circle is 14 cm. Find the distance from the center of the circle to the chord

The radius of the circle is 14 cm. Find the distance from the center of the circle to the chord that contracts the arc of 120 degrees.

Let’s introduce the notation:
AB is the chord, O is the center of the circle, the angle contracting the chord AOB = 120 °, OA = OB = 14 cm is the radius of the circle.
Consider an isosceles triangle AOB (OA, OB – radii). In it, you need to find the height OH, which will be the distance from the center of the circle to the chord AB.
Consider a right-angled triangle AOН, in which the hypotenuse OA and acute angles are known:
∠О = 120 ° / 2 = 60 °;
∠А = 90 ° – 60 ° = 30 °.
The OH leg lies opposite the angle A, the degree measure of which is 30 °, which means that it is equal to half the hypotenuse:
OH = 1/2 * OA = 1/2 * 14 = 7 (cm).
Answer: 7 cm.