CAT Quant Practice Problems

Question: In \(\Delta ABC\), the internal bisector of \(\angle A\) meets \(BC\) at \(D\). If\(AB{\rm{ }} = {\rm{ }}4, {\rm{ }}AC{\rm{ }} = {\rm{ }}3{\rm{ }} \;and \;\angle A = 60^\circ \), then the length of \(AD\) is

\(2\sqrt 3 \)
\(\frac{{12\sqrt 3 }}{7}\)
\(\frac{{15\sqrt 3 }}{8}\)
\(\frac{{6\sqrt 3 }}{7}\)
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