Question

In the given fugure, AD is the bisector of ∠BAC. If AB = 10 cm, AC = 14 cm and BC = 6 cm. Find BD and DC.
[3 Marks]

Answer 1

Let BD = x cm, then DC = (6 - x) cm.
Since AD is the bisector of ∠A.

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ∴ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\frac{AB}{AC}$ = $\frac{BD}{DC}$ [By Angle Bisector Theorem]

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\Rightarrow$ $\frac{10}{14}$ = $\frac{x}{6-x}$ [1 Mark]

$\Rightarrow$ $\frac{5}{7}$ = $\frac{x}{6-x}$

$\Rightarrow$ 30 - 5x = 7x
$\Rightarrow$ 12x = 30

$\Rightarrow$ x = $\frac{5}{2}$ = 2.5 cm [1 Mark]

$\Rightarrow$ BD = 2.5 cm and DC = (6 - x) cm = (6 - 2.5) cm = 3.5 cm [1 Mark]