Question 3

# In $$\triangle$$ ABC, AB = 12 cm. $$\angle$$ A is bisected internally to intersect BC at D. BD = 7 cm and DC = 8.75 cm. What is the length of CA ?

Solution

Triangle Angle Bisector Theorem. An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle

So ,

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

$$\frac{12}{AC} = \frac{7}{8.75}$$

AC = $$\frac{12 \times 8.75}{7}$$ = 15

So , the answer would be option b)15 cm