Geometry

Question Analysis

This question hinges on the Triangle Perpendicular Bisector Concurrence Theorem. The main goal is to determine which segment is equal to  given that  is the circumcenter. The key is leveraging the property that the circumcenter is equidistant from all vertices of the triangle.

 

Key Concept Explanation

Circumcenter: The circumcenter is the point where the perpendicular bisectors of a triangle's sides intersect. It serves as the center of the circum - circle that passes through all three vertices of the triangle. A defining characteristic of the circumcenter is its equidistance from all 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 .

 

Option Analysis

A. NI: Incorrect.  is not a vertex, so  does not represent the distance from the circumcenter to a vertex and is not equal to .

B. NH: Correct. As

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