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Question

In $$ \triangle$$ ABC, the bisector of  $$\angle$$  A intersects BC  in D. If AB = 18 cm, AC = 15 cm and BC = 22 cm, find BD.


Solution

Given $$AB = 18$$ cm, $$AC = 15$$ cm and $$BC = 22$$ cm

By angle bisector theorem, if bisector of $$\angle A$$  meets side $$BC$$ at $$D$$, then  

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

$$\dfrac {AB} {AC} =\dfrac {BD} {BC-BD} $$

Substituting values of $$AB, AC$$ and $$BC$$

$$ \dfrac {18}{15}=\dfrac {BD} {22-BD}$$

$$\dfrac {6}{5}=\dfrac {BD}{22-BD}$$

$$(22*6) -6BD = 5BD$$

$$\therefore BD=12$$cm.

Mathematics

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