Question 53
In $$\triangle ABC, AD$$ is the bisector of $$\angle A$$ meeting BC at D. If AB = 15 cm, BC = 10 cm and the length of BD is 2 cm less than that of DC, then the length of AC is:
Solution
BD = DC - 2
and BD + DC = 10.
This gives BD = 4 cm and DC = 6 cm.
Using angle bisector theorem:
$$\frac{AB}{AC}=\frac{BD}{DC}$$
==> $$\frac{15}{AC}=\frac{4}{6}$$
==> AC = 22.5 cm.
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