Someone must be telling the truth, or else 33 liars would all be claiming that the next ten people are liars—and they would all be correct.
If Person A tells the truth, then A is correct that the next ten people are all liars:
In particular, we know that Person B, the person on Person A's right side, is a liar. Person B claims that the next ten people are all liars:
Person B must be wrong about that claim, because Person B is a liar. The first nine people are liars because A said they were. This implies that the last person isn't a liar --- the tenth person after B is honest:
and now the reasoning repeats again with a new truth teller. In the end, you're left with three equally-spaced truth-tellers amidst 30 liars.
In general, you can have a circle of $n$ people claiming that the next $k$ people are all liars. If $n$ is a multiple of $k+1$, then the situation is solvable: there's one truth teller followed by $k$ liars, followed by a truth teller, etc. If $n$ isn't a multiple of $k+1$, then you can't solve the problem in Truthlandia. (Compare two versus three people sitting around a table all claiming that the next person is a liar. The situation is solvable with two people, but not with three.)