In a $\triangle\text{ABC},\text{AD}$ is the bisector of $\angle\text{A}.$
If AB = 5.6cm, AC = 4cm and DC = 3cm, find BC.
If AB = 5.6cm, AC = 4cm and DC = 3cm, find BC.
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It is given that AD bisects $\angle\text{A}.$
Applying angle-bisector theorem in $\triangle\text{ABC},$ we get:
$\frac{\text{BD}}{\text{DC}}=\frac{\text{AB}}{\text{AC}}$
$\Rightarrow\frac{\text{BD}}{3}=\frac{5.6}{\text{4}}$
$\Rightarrow\text{BD}=\frac{5.6\times3}{4}$
$\Rightarrow\text{BD}=4.2\text{cm}$
Hence, BC = 3 + 4.2 = 7.2cm
Applying angle-bisector theorem in $\triangle\text{ABC},$ we get:
$\frac{\text{BD}}{\text{DC}}=\frac{\text{AB}}{\text{AC}}$
$\Rightarrow\frac{\text{BD}}{3}=\frac{5.6}{\text{4}}$
$\Rightarrow\text{BD}=\frac{5.6\times3}{4}$
$\Rightarrow\text{BD}=4.2\text{cm}$
Hence, BC = 3 + 4.2 = 7.2cm
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