解:$(1)$因为$AD = 6,$$BD = 4,$
根据线段的和的关系,$AB=AD + BD,$
所以$AB = 6 + 4 = 10。$
$ $因为$C$是线段$AB$的中点,
根据线段中点的定义,$BC=\frac {1}{2}AB,$
所以$BC=\frac {1}{2}×10 = 5。$
$ (2)$由$(1)$知$BC = 5,$
又因为$BD = 4,$
根据线段的差的关系,$CD = BC - BD,$
所以$CD = 5 - 4 = 1。$