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Question

In the figure given below AD is bisector of BAC. If AB=6 cm,AC=4 cm and BD=3 cm, find BC.
1164689_24ff339af2fa4e74a099809ff3f8ac3f.jpg

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Solution

From the question it is given that,
AD is bisector of BAC
AB=6cm,AC=4cm and BD=3cm
Construction, from C draw a straight line CE parallel to DA and join AE
1=2 … [equation (i)]
By construction CEDE
So, 2=4 … [because alternate angles are equal] [equation (ii)]
Again by construction CEDE
1=3 … [because corresponding angles are equal] [equation (iii)]
By comparing equation (i), equation (ii) and equation(iii) we get,
3=4
So, AC=AE … [equation (iv)]
Now, consider the BCE,
CEDE
BD/DC=AB/AE
BD/DC=AB/AC
3/DC=6/4
By cross multiplication we get,
3×4=6×DC
DC=(3×4)/6
DC=12/6
DC=2
Therefore, BC=BD+DC
=3+2
=5cm.
1700033_1164689_ans_b7db06a0871945c7a0336dd590204de8.PNG

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