Zigzag

Level pending

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+...)

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