If a circle of unit radius is divided into two parts by an arc of another circle subtending an angle 60∘ on the circumference of the first circle, then the radius of the arc is:
Solutions · 1
Official solution
If a chord of the unit circle subtends 60∘ at the circumference, it subtends 120∘ at the centre, so the chord length is 2sin60∘=3. The arc (of the second circle) passing through the same two chord endpoints and subtending 60∘ at *its own* circumference has this chord subtending 120∘ at its centre too, giving the same relation: radius =2sin60∘chord=33⋅ --- working through the standard result for this classic construction, the radius of the arc is 3.