In a $\triangle\text{ABC},\text{AD}$ is the bisector of $\angle\text{A}.$ If AB = 5.6cm, BD = 3.2cm and BC = 6cm, find AC.
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It is given that AD bisects $\angle\text{A}.$
Applying angle-bisector theorem in $\triangle\text{ABC},$ we get:
$\frac{\text{BD}}{\text{DC}}=\frac{\text{AB}}{\text{AC}}$
BD = 3.2cm, BC = 6cm
Therefore, DC = 6 - 3.2 = 2.8cm
$\Rightarrow\frac{3.2}{2.8}=\frac{5.6}{\text{AC}}$
$\Rightarrow\text{AC}=\frac{5.6\times2.8}{3.2}=4.9\text{cm}$
Applying angle-bisector theorem in $\triangle\text{ABC},$ we get:
$\frac{\text{BD}}{\text{DC}}=\frac{\text{AB}}{\text{AC}}$
BD = 3.2cm, BC = 6cm
Therefore, DC = 6 - 3.2 = 2.8cm
$\Rightarrow\frac{3.2}{2.8}=\frac{5.6}{\text{AC}}$
$\Rightarrow\text{AC}=\frac{5.6\times2.8}{3.2}=4.9\text{cm}$
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