Geometry

Question Analysis

This question is centered around the Triangle Perpendicular Bisector Concurrence Theorem. The main focus is to utilize the property of the circumcenter to determine which segment is equal to .

 

Key Concept Explanation

Circumcenter: The circumcenter of a triangle is the point of intersection of the perpendicular bisectors of the triangle's sides. A fundamental property of the circumcenter is that it is equidistant from all the vertices of the triangle. This is because the circumcenter is the center of the circum - circle that passes through all three vertices of the triangle.

 

Step-by-Step Solution

Recall the property of the circumcenter: Since  is the circumcenter of , by definition,  is equidistant from all the vertices , , and .

 

Option Analysis

A. GD: Incorrect.  is a segment on the perpendicular bisector of