How informed flow sets the spread

An asset's true value is either $V_H = 110$ or $V_L = 90$, each equally likely. A fraction $\alpha$ of the traders who arrive are informed (they know $V$ and always trade the profitable direction); the remaining $1-\alpha$ are noise traders who buy or sell $50/50$ at random. You are a competitive market maker who must post a bid and an ask before seeing who arrives.

At what ask (and bid) do you break even? Show how the spread depends on $\alpha$.