### Question 17

SSC-CGL 2020 Mar 3 Shift 2

In a triangle ABC, AP is an angle bisector and AB = 4, AC = 6, and BP = 3. The length of CP is?

### Solution in Brief

By the angle bisector theorem,

$\displaystyle \frac{PC}{AC} = \frac{BP}{AB}$

$\displaystyle \therefore \frac{x}{6} = \frac 34$

$\displaystyle \implies x = 4.5 \:\underline{Ans}$

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