What will the angle made by the two radii at the centre of a circle, if the angle made by two tangents from the endpoints of this radius is $60$ degrees?

The radius drawn to a tangent is always perpendicular to the tangent line. This forms a right-angled triangle with the radius, the tangent segment, and the line from the center to the external point. The angle between the tangent and this external line is half of 60 degrees, which is 30 degrees. Therefore, the angle at the center between the two radii is 90 degrees plus 30 degrees, resulting in 120 degrees.

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