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 $$BC = 22$$ cmBy 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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