Question 57
In $$\triangle$$ ABC,D is a point on BC such that AD is the bisector of $$\angle$$ A, AB = 11.7 cm, AC = 7.8 cm and BC = 13 cm. What is the length (in cm) of DC?
Solution
By the angle bisector theorem,
$$\frac{DC}{AC} = \frac{BD}{AB}$$
$$\frac{DC}{7.8} = \frac{13 - DC}{11.7}$$
$$11.7 \times DC = 7.8(13 - DC)$$
DC = 101.4/19.5 = 5.2 cm
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