Problem 9

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Problem 9: (2018 AMC12B, 12)

Side $\overline{AB}$ of $\triangle ABC$ has length $10$. The bisector of angle $A$ meets $\overline{BC}$ at $D$, and $CD = 3$. The set of all possible values of $AC$ is an open interval $(m,n)$. What is $m+n$?
$\textbf{(A) }16 \qquad$ $ \textbf{(B) }17 \qquad$ $ \textbf{(C) }18 \qquad$ $ \textbf{(D) }19 \qquad$ $ \textbf{(E) }20 \qquad$

Solution

Exercise 9: Solution

Side $\overline{AB}$ of $\triangle ABC$ has length $21$. The bisector of angle $A$ meets $\overline{BC}$ at $D$, and $CD = 4$. The set of all possible values of $AC$ is an open interval $(m,n)$. What is $m+n$?

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