# Trisected Triangle

Geometry Level 4

In acute triangle $$ABC$$, $$O$$ is an interior point. The perpendiculars from $$O$$ to sides $$BC, CA$$ and $$AB$$ intersect the respective sides at $$D, E$$ and $$F$$. Given that $$FA = 12, AE =8, EC = 13$$, $$CD = 11, DB = 14$$, what is the length of $$BF$$?

×