Final answer:
Perpendicular bisectors in a triangle intersect at the circumcenter, equidistant from the vertices, forming the basis of the circumcenter theorem.
Explanation:
Perpendicular bisectors of the sides of a triangle are lines that are perpendicular to the sides and pass through the midpoints of those sides. These bisectors intersect at a point called the circumcenter, which is equidistant from the vertices of the triangle.
The circumcenter is the center of the circumscribed circle that can be drawn to pass through all three vertices of the triangle. This property forms the basis of the circumcenter theorem in geometry.
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