Question 93

The bisector of $$\angle A$$ in $$\triangle ABC$$ meets $$BC$$ in $$D$$. If $$AB = 15 cm, AC = 13 cm$$ and $$BC = 14 cm$$, then $$DC = ?$$

Solution

From the angle bisector theorem-

$$\frac{AB}{BD} = \frac{AC}{DC}$$

BD = BC - DC

$$\frac{AB}{BC - DC} = \frac{AC}{DC}$$

$$\frac{15}{14 - DC} = \frac{13}{DC}$$

$$\Rightarrow 15 \times DC = 13 \times 14 - 13 \times DC$$

$$\Rightarrow 28 \times DC = 182$$

$$\Rightarrow DC = 6.5 cm

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