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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