# How many centroids do we need?

Geometry Level 3

Let $$P$$ be any point inside a triangle $$ABC$$. We further denote
- $$L$$ as the centroid of the triangle $$PBC$$.
- $$M$$ as the centroid of the triangle $$PAC$$.
- $$N$$ as the centroid of the triangle $$PAB$$.

What is the ratio of area of triangle $$ABC$$ to the area of triangle $$LMN$$?

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