$20 \cdot 75$ For any $\triangle ABC$, let its perimeter, the radius of the circumcircle, and the radius of the incircle be $l, R$, and $r$, respectively. Then
(A) $l>R+r$.
(B) $l \leqslant R+r$.
(C) $\frac{l}{6}<R+r<6 l$.
(D) None of the above (A), (B), (C) is correct.
(China High School Mathematics League, 1983)
[Solution] First, draw a circle with radius $R$ (as shown in the right figure). For any positive integer $N$, we can always take three points $A, B, C$ on the circumference of this circle that are sufficiently close to each other, such that $N lR$, $BC > R$, and then connect $A C$, then $l > 2R > R + r$. This shows that
(B) does not necessarily hold.
Therefore, the answer is $(D)$.