Question 50

In $$\triangle$$ ABC, AB = 8 cm. $$\angle$$A is bisected internally to intersect BC at D. BD = 6 cm and DC = 7.5 cm. What is the length of CA?

Solution

Given,

In triangle △ ABC,

$$AB = 8 cm$$, $$BD = 6 cm$$ and $$DC=7.5cm$$

angle ∠A is bisected internally to intersect BC at D

By using angle bisector theorem

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

$$AC=\frac{\left(AB\cdot DC\right)}{BD}$$

$$AC= \frac{\left(8\star 7.5\right)}{6}$$

$$AC= \frac{60}{6}$$

$$AC= 10 cm$$

Create a FREE account and get: