  We study implications of a recent observation of non-leptonic $B^+_c\to D^0
K^+$ decay and a bound on $B^+_c\to D^0 \pi^+$ transition on CP-violating
asymmetries in $B_c$ decays. In the U-spin symmetry limit, we derive a relation
between the CP-asymmetries in the $B^+_c\to D^0 K^+$ and $B^+_c\to D^0 \pi^+$
channels and the corresponding branching ratios. We also derive several
relations between non-leptonic $B_c$ decays into the final states with $D$
mesons in the flavor $SU(3)_F$ limit. We point out that a combined study of
$SU(3)_F$ amplitudes in these decays can be used to constrain the angle
$\gamma$ of the Cabibbo-Kobayashi-Maskawa (CKM) matrix.
