Geometry

Question Analysis

This question relies on the Triangle Perpendicular Bisector Concurrence Theorem. The key is to use the property of the circumcenter to determine which segment is equal to .

 

Key Concept Explanation

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

 

Option Analysis

A. EC: Incorrect.  is a side of the triangle and not related to the distance from the circumcenter to a vertex.

B. BC: Incorrect.

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