Combining CP Asymmetries in $B \to K π$ Decays

We prove an approximate equality, to leading order in dominant terms, between CP-violating rate differences in $B^0/\bar{B}^0 \to K^{\pm}\pi^{\mp}$ and $B^{\pm} \to K^{\pm}\pi^0$. We propose several versions of averaged asymmetry measurements in these two processes, for which present data are already capable of yielding a statistically significant nonzero result in the most favorable case of weak and strong phases.