Gybrisysmemiau7

2022-06-26

If I have triangle ABC with side lengths a,b,c, and I have an angle bisector coming out of point A, which divides side a into two sections at intersection point P, what is the length of BP and PC?

Lisbonaid

Beginner2022-06-27Added 22 answers

This is well known property of bisector. $\frac{BP}{CP}=\frac{AB}{AC}$. So you have a system

$\frac{BP}{CP}=\frac{b}{c}$ and $BP+PC=a$

The solution to the system is $BP=\frac{ac}{b+c}$ and $CP=\frac{ab}{b+c}$

$\frac{BP}{CP}=\frac{b}{c}$ and $BP+PC=a$

The solution to the system is $BP=\frac{ac}{b+c}$ and $CP=\frac{ab}{b+c}$

fabios3

Beginner2022-06-28Added 10 answers

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