Question

in triangle abc the bisector of angle a intersects bc at d. if ab = 8, ac= 10 and bd = 3.2 find bc​

Answer 1

$\textbf{Given:}$

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

$\mathsf{AB=8,\;AC=10,\;BD=3.2}$

$\textbf{To find:}$

$\textsf{BC}$

$\textbf{Solution:}$

$\textbf{Angle bisector theorem:}$

$\text{When vertical angle of a triangle is bisected,}$

$\text{the bisector divides the base into two segments}$

$\text{which have the ratio as the order of other two sides}$

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

$\textsf{By Angle bisector theorem, we  get}$

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

$\mathsf{\dfrac{3.2}{DC}=\dfrac{8}{10}}$

$\mathsf{8\;DC=32}$

$\mathsf{DC=\dfrac{32}{8}}$

$\implies\boxed{\mathsf{DC=4}}$

$\mathsf{Now,}$

$\mathsf{BC=BD+DC=3.2+4=7.2}$

$\textbf{Answer:}$

$\textsf{BC is 7.2 cm}$

$\textbf{Find more:}$

In ∆ABC , AD the bisector of angle A meets BC at D. If BC=a, AC=b ,AB=c

then BD-DC​

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Answer 2

Given info : in triangle abc the bisector of angle a intersects bc at d. if ab = 8, ac = 10 and bd = 3.2.

To find : The value of bc is ...

solution : from angle bisector theorem, if angle bisector of A meets the side BC at D then,

AB/AC = BD/DC

here AB = 8 , AC = 10, BD = 3.2

so, 8/10 = 3.2/DC

⇒4/5 = 3.2/DC

⇒DC = 3.2 × 5/4 = 4

Therefore the value of DC = 4 unit.

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