In $\triangle ABC$, $DE \parallel BC$ intersects $AB$ at $D$ and $AC$ at $E$. If $AD = 3\text{ cm}$, $DB = 6\text{ cm}$, and $AE = 4\text{ cm}$, find the length of $AC$.
Options:
- A: 12 cm
- B: 8 cm
- C: 9 cm
- D: 10 cm
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