I don't see a pic, but I assume that the arc in question is spanned by the chord......if so
60° arc - the radius = (1/2 chord length)/ sin (30) = 5 / (1/2) = 10
90° arc - the radius = (1/2 chord length) / sin (45) = 5√2
180° arc - the radius = (1/2) chord length) = 5