Question

In triangle ABC, AP is an angle bisector of angle BAC. What is the length of PC? Round you answer to the nearest whole number.

A) 6
B) 7
C) 8
D) 9

Answer 1

D

Explanation:

the angle bisector divides the opposite side into segments that are proportional to the other 2 sides.

note that BP = 16 - PC , then

`(BP)/(PC)` =
`(AB)/(AC)` ( substitute values )

`(16-PC)/(PC)` =
`(8)/(10)` =
`(4)/(5)` ( cross- multiply )

4 PC = 5(16 - PC) ← distribute parenthesis

4 PC = 80 - 5 PC ( add 5 PC to both sides )

9 PC = 80 ( divide both sides by 9 )

PC = 8.888... ≈ 9 ( to the nearest whole number )

Answer 2

The length of PC is 6

Sure hope this helps you :D