6 Place some small circles with a radius of 1 inside a large circle with a radius of 11, so that each small circle is internally tangent to the large circle, and these small circles do not overlap. Then the maximum number of small circles that can be placed is ( ).
(A) 30
(B) 31
(C) 32
(D) 33
(6) B Hint: As shown in the figure, let the center of the large circle be $O$. The two small circles $A$ and $B$ are tangent to each other. In $\triangle A O B$, $A B=2, A O=$ $B O=10$. Then $\sin \frac{\angle A O B}{2}=\frac{1}{10}, \tan \frac{\angle A O B}{2}=$ $\frac{1}{\sqrt{99}}$.
Since for $x \in\left(0, \frac{\pi}{2}\right)$, $\sin x < x < \tan x$.
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It is known that placing 32 circles must result in at least two circles overlapping. Therefore, the answer is B.