# Zigzag

In triangle **ABC**,** AB=54 , **

**BC=45**,

**AC=36**. Point

**D**is on

**AB**such that

**CD**bisects angle

**ACB**,point

**E**is on

**AC**such that

**DE**bisects angle

**ADC**, point

**F**is on

**AD**such that

**EF**bisects angle

**AED**, and the process is continued indefinitely. What is the sum of the angle bisectors? (

**CD+DE+EF+FG+...**)