The centroid is the point of concurrency of the medians of a triangle. In the given diagram, P is the centroid.
Using the Concurrency of Medians Theorem, we can write an equation that we can use to find the desired length PC.
PC = 2/3CF
We are given that PF=6. To use this information, we should rewrite CF as the sum of two smaller segments PC and PF considering the Segment Addition Postulate.
PC = 2/3CF ⇒ PC = 2/3(PC+PF)
Now, we can solve the resulting equation to find PC.
