The arc BD of a circle is 60 °. The radius of the circle is 32. Find the chord length BD.

First, construct an angle BOD = 60 (central, rests on an arc of 60 degrees) and a chord BD. The result is a triangle BOD. Consider it:
Since the angle BOD = 60, and BO = OD (radii), then the angles at the base are equal, that is, the angle DBO = the angle BDO and is equal to (180-60) / 2 = 60 degrees d, therefore the triangle BOD is equilateral and all its sides are equal each other. Hence BD = 32.
Answer: 32