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Question: Answered & Verified by Expert
Let $A B C$ be an acute-angled triangle and let $D$ be the midpoint of $B C$. If $A B=A D$, then $\tan (B) / \tan (C)$ equals
MathematicsProperties of TrianglesKVPYKVPY 2013 (SB/SX)
Options:
  • A $\sqrt{2}$
  • B $\sqrt{3}$
  • C 2
  • D 3
Solution:
2867 Upvotes Verified Answer
The correct answer is: 3


Using M - N Rule
$$
\begin{array}{l}
(1+1) \cot (\pi-B)=1 \cdot \cot B-\cot C \\
3 \cot B=\cot C \\
\frac{\tan B}{\tan C}=3
\end{array}
$$

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