Geometry

Question Analysis

This question is firmly rooted in the Triangle Perpendicular Bisector Concurrence Theorem. The principal aim is to correctly name the point of concurrency formed by the three perpendicular bisectors of a triangle.

Key Concept Explanation

1. Perpendicular bisectors: A perpendicular bisector of a side in a triangle is a line that is perpendicular to the side and passes through its mid - point. The Triangle Perpendicular Bisector Concurrence Theorem states that the three perpendicular bisectors of a triangle's sides intersect at a single point.

2. Points of concurrency in triangles: Different sets of lines in a triangle—such as medians, angle bisectors, altitudes, and perpendicular bisectors—intersect at distinct points of concurrency, each with unique properties.

Step-by-Step Solution

A. Midsegment: Incorrect. A midsegment is a line segment that connects the mid - points of two sides of a triangle, not a point of concurrency.

B. Incenter: Incorrect. The incenter is the point of concurrency of the angle bisectors of a triangle, not perpendicular bisectors.

C. Circumcenter: Correct. The circumcenter is defined as the point where the three perpendicular bisectors of a triangle's sides intersect.

D....