Diameter BD is drawn in a circle centered at point O. And the radius is OK, with the chord DK = OK

Diameter BD is drawn in a circle centered at point O. And the radius is OK, with the chord DK = OK. Find the BOK angle if the KDB angle is 60 degrees.

Since, according to the condition, OK = DK, then the triangle ODK is equilateral, and since OK = OD as the radii of the circle, then OK = OD = DK, then the triangle ODK is equilateral and all its internal angles are 180. The angles BOK and DOK are adjacent, then their sum is 180, which means that the angle BОК = 180 – 60 = 120.
Answer: The value of the angle BОК is equal to 120.