Question

In ∆ABC,AD is an angle bisector.If AB=18cm ,AC=24cm and BD=12,then find CD​

Answer 1

$\textbf{Given:}$

$\mathsf{In\,\triangle\,ABC,\;AD\;is\;the\;bisector}$

$\mathsf{AB=18cm,\;AC=24cm\;and\;BD=12cm}$

$\textbf{To find:}$

$\textsf{Length of CD}$

$\textbf{Solution:}$

$\textbf{Concept used:}$

$\boxed{\begin{minipage}{11cm} \underline{\mathsf{Angle\;bisector\;theorem:}}\\\\\textsf{When vertical angle of a triangle is bisected, the bisector divides the base}\\\\\textsf{into two segments which have the ratio as the order of other two sides.}\\ \end{minipage}}$

$\mathsf{In\;\triangle\,ABC,\;AD;is\;the\;bisector\;of\;\angle{A}}$

$\mathsf{By\;angle\;bisector\;theorem,}$

$\mathsf{\dfrac{BD}{CD}=\dfrac{AB}{AC}}$

$\mathsf{\dfrac{12}{CD}=\dfrac{18}{24}}$

$\mathsf{\dfrac{12}{CD}=\dfrac{3}{4}}$

$\mathsf{\dfrac{4}{CD}=\dfrac{1}{4}}$

$\mathsf{CD=4{\times}4}$

$\implies\boxed{\mathsf{CD=16\,cm}}$

$\textbf{Find more:}}$

AD=15 and DC=20. If BD is the bisector of angle ABC, what is the perimeter of the triangle ABC?

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The sides of a triangle are 28 cm, 36 cm and 48 cm. Find the lengths of line segments into which the smallest side is divided by the bisector of the angle opposite to it

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