Analysis of a VDB circuit
You have used 0.7 volts as the base-emitter volt drop - this is an over-simplification. For instance, if you look at the data sheet for the 2N3904 it tells you that the base-emitter voltage might be as high as 0.85 volts with 1 mA flowing into the base and 0.95 volts with 5 mA flowing: -



So, it's more complex/subtle than what you thought but who's really going to get in a pickle about 0.13 volts difference on a single transistor circuit?

On this occasion to work out what Vc is you have to realize the transistor is saturated and regard the collector-base region as potentially forward biased - in other words, the collector voltage cannot be lower than the base voltage by more than a volt and so 9.2 volts sounds reasonable.