Question 51

The perimeter of $$ \triangle$$ ABC is 24 cm and its side, BC = 9 cm. AD is the bisector of $$ \angle BAC$$, while I is the incentre. AI : ID is equal to:

Solution

Perimeter of Triangle ABC= AB + BC + AC = 24

AB + AC = 24 - 9 = 15

Using the theorem , $$\frac{AI}{ID}=\frac{\left(AB+AC\right)}{BD}$$

$$\frac{AI}{ID}$$= $$\frac{\left(AB+AC\right)}{9}=\frac{15}{9}$$

$$\frac{AI}{ID}$$ = $$\frac{15}{9}=\frac{5}{3}$$

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