Lets say I have three variables, A, B, and C. I can of course calculate the correlation between any of them (and have these numbers). However what I'm interested in is if there's a bound on the correlation of A and C plus B and C, $r_{A,C}$ + $r_{B,C}$, given $r_{A,B}$. Intuitively it seems like there should be one, but I'm not sure. Does anyone know?
Alternatively, could we find a bound for $r_{A,C}$ $\cdot $ $r_{B,C}$?