# Circumcentre has another name if you play inside

Geometry Level 4

Given $$G$$ is the circumcentre of $$\triangle ABC$$. Let $$D$$, $$E$$ and $$F$$ be respectively the points on $$BC$$, $$AC$$ and $$AB$$ such that $$GD \perp BC$$, $$GE \perp AC$$ and $$GF \perp AB$$. Then what is the necessary geometric relation between $$G$$ and $$\triangle DEF$$?

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