A chord of a circle of radius 10 cm subtends an angle of 60° at the centre. The length of the chord is:

Drop a perpendicular from the centre to the chord: it halves both the chord and the central angle, so chord = $2R$·sin(θ/2) = 2(10)·sin30° = 10 cm. (The two radii and the chord form an equilateral triangle, which confirms it.) Forgetting to halve the angle gives $2R$·sin60° = 10√3 ≈ 17.3 cm, longer than the radius pair allows for a 60° opening.