**Definition of the circumcenter of a triangle:**

The** **circumcenter of a triangle in the
point in the same plane as the triangle that is equidistant from
the three vertices of the triangle. We know the perpendicular
bisector of a segment is equidistant from the endpoints of the
segment. Thus, the circumcenter of a triangle is where the perpendicular
bisectors of the three sides of the traingle intersect. However,
it remains to show all three perpendicular bisectors intersect.

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