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Question 62
In $$\triangle$$ABC, AD is the bisector of $$\angle$$BAC, meeting BC at D. If AC = 21 cm, BC = 12 cm and the length of BD is 2 cm less than DC, then the length of side AB is:Â
Solution
BC = 12
Let DC= x then BD = x-2
x + x-2=12
x = 7
BD = 5 and DC=7
By angle bisector theorem,
$$\frac{AB}{AC}=\frac{BD}{DC}$$
$$\frac{AB}{21}=\frac{5}{7}$$
AB=15 cm
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