Geometry

Question Analysis

This question is based on the Triangle Perpendicular Bisector Concurrence Theorem. The core task is to determine which segment is equal to  given that  is the circumcenter of the triangle. The key lies in understanding the property of the circumcenter being equidistant from the vertices of the triangle.

 

Key Concept Explanation

Circumcenter: The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. It serves as the center of the circum - circle that passes through all three vertices of the triangle. A fundamental property of the circumcenter is that it is equidistant from all the vertices of the triangle.

 

Step-by-Step Solution

Recall the property of the circumcenter: Since  is the circumcenter, it is equidistant from all vertices of the triangle.

 

Option Analysis

A. UO: Correct. As  is the circumcenter and  is a vertex,  is equal to

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