In BCC nearest neighbours are atoms at A and D.
The Distance AB = (square root of 3) a
So AD = Half of AB = [(square root of 3) a] / 2
So radius r = Half of the distance between nearest neighbours
i.e. radius r = [(square root of 3) a] / 4
So lattice constant a = 4r / (square root of 3)

In FCC nearest neighbours are atoms at A and D.
The Distance AB is (square root of 2) a
So AD = Half of AB = [(square root of 2) a] / 2
So radius r = Half of the distance between nearest neighbours
i.e. radius r = [(square root of 2) a] / 4
So lattice constant a = 4r / (square root of 2)