The following data refers to a symmetrical circular arc cam operating a flat-faced follower: Least radius of cam \(=30 \mathrm{~mm}\), Lift \(=12.5 \mathrm{~mm}\), Angle of lift \(=55^{\circ}\), Nose radius \(=3 \mathrm{~mm}\), Speed of cam \(=600 \mathrm{rpm}\). Calculate

(a) distance between cam and nose centres,

(b) radius of circular flank, and

(c) angle of contact on the circular flank.