What Point Is This?

Geometry Level 3

Let \(ABC\) be any triangle, prolong the sides so that segments of the same color have the same length.

It can be shown that the six exterior points belong to the same circle \(\Gamma\) [Try to prove this fact!]. Then complete the following sentence:

The center of \(\Gamma\) is the \(\ldots \ldots \ldots\) of triangle \(ABC\).

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