Question

In a ΔABC, AD is the bisector of ∠A, meeting side BC at D. If BD = 2.5 cm, AB = 5 cm, and AC = 4.2 cm, find DC.
[2 Marks]

Answer 1

Since,
AD is the bisector of ∠A meeting side BC at D in Δ ABC

Therefore,
$\frac{AB}{AC}=\frac{BD}{CD}$ [Using Angle Bisector Theorm]
[1 Mark]

⇒ $\frac{5}{4.2}=\frac{2.5}{CD}$

⇒ $5\times CD=2.5\times 4.2$

⇒ $CD=2.1cm$

$\therefore$ DC = 2.1 cm.
[1 Mark]