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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
$$\frac{AB}{AC}=\frac{BD}{DC}$$
$$AC=\frac{\left(AB\cdot DC\right)}{BD}$$
$$AC= \frac{\left(8\star 7.5\right)}{6}$$
$$AC= \frac{60}{6}$$
$$AC= 10 cm$$
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