20.49 An equilateral triangle $ABC$ is inscribed in circle $O, M$ is on $BC$, connect segments $AM, BM$ and $CM$, then $AM$
(A) equals $BM + CM$.
(B) is less than $BM + CM$.
(C) is greater than $BM + CM$.
(D) equals, is greater than, or is less than $BM + CM$ depending on the position of $M$.
(E) none of the above.
[Solution] On $AM$, intercept $MD = MC$, and connect $CD$. Then $\triangle MCD$ is an equilateral triangle.
$$
\therefore CD = MC \text{, and } AC = BC \text{, }
$$

and $\angle CAM = \angle CBM$,
then $\triangle ADC \cong \triangle BMC$. Thus, $AD = MB$,
$$
\therefore \quad AM = MB + MC \text{. }
$$

Therefore, the correct choice is $(A)$.