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
Get AI Help
Video Solution
Click on the Email ☝️ to Watch the Video Solution
Create a FREE account and get:
- Free SSC Study Material - 18000 Questions
- 230+ SSC previous papers with solutions PDF
- 100+ SSC Online Tests for Free
