Geometry

Question Analysis

This question is about applying the Triangle Perpendicular Bisector Concurrence Theorem. The main idea is to use the property of the circumcenter (the point where perpendicular bisectors intersect) which is equidistant from the vertices of the triangle.

 

Key Concept Explanation

The circumcenter of a triangle is the point of intersection of the perpendicular bisectors of the triangle's sides. A key property is that it is equidistant from all vertices. So, if  is the circumcenter of , then .

 

Step - by - Step Solution

1. Since  is the circumcenter (where perpendicular bisectors meet), by its property, the distances from  to vertices ,

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